research methods – Page 6

ARTICLE 40: Research Methods for Ph. D. and Master’s Degree Studies: Statistical Research Methods Part 2 of 2

8th Sep 2020 No Comments

Written by Dr. Hannes Nel

Introduction

It is said that Albert Einstein wrote in a letter to his daughter in 1938 that there is an extremely powerful force that governs all the universe, a variable that scientists often forget.

He confessed that he omitted the variable when he developed the relativity theory.

That variable is love.

I don’t know if the story is true.

And if it is true, then Einstein probably wrote a letter to his daughter in which he declared his love for her in a most romantic and creative manner.

Even so, it made me think. When scientists start their findings by writing: “all other factors being constant,” they are admitting that their findings are wrong.

Because other factors are never constant.

I guess I am just being difficult because it is sometimes necessary to investigate the influence of single factors on an event, behaviour or phenomenon.

Even so, the need for considering the interrelationship between different factors are also important.

I will discuss the following issues related to statistical research methods in this article:

Determining validity from statistical data.
Calculating statistical significance.
Analyzing statistics.
Coming to conclusions from statistical data.

Determining validity from statistical data

Statistical validity refers to whether conclusions drawn from a statistical study agree with statistical and scientific laws.

There are different kinds of statistical validities that are relevant to research.

The following are examples of such statistical validities.

Construct validity. Construct validity ensures that the results of the data that you collected conform to the theory of your research.

For example, a questionnaire on the quality of learning provided by universities and completed by employers must provide a true picture of the value that university studies have for the workplace.

Content validity. Content validity ensures that the test or questionnaire that you prepared covers all aspects of the variable that is being studied.

For example, if you were to do research on the exam papers that students studying towards a degree in accounting must write, then the exam papers must test all the exit level outcomes of the subject to have content validity.

Face validity. Face validity is related to content validity and is a quick initial estimate to check if the test that you will conduct is in line with the hypothesis that you are investigating. It is more subjective than content validity.

For example, if you were to do research on the exam papers that students studying towards a degree in accounting must write, and it looks like a good exam paper that meets the requirements for assessment, then on appearance the exam papers can have face validity.

Conclusion validity. Conclusion validity is achieved when the conclusions that you reach from the data that you collected are accurate and justified.

This will be the case if the sample or samples that you used are large enough, randomly chosen and taken from the population being investigated.

Criterion validity. Criterion validity measures how closely the results that you obtain with a data collection instrument matches that of a different instrument.

For example, if you use a questionnaire to measure the extent to which university studies add value to the workplace, and you measure the same research question by making use of a different, proven questionnaire that was used for the same purpose previously, then your questionnaire will have criterion validity if it delivers the same results, or at least nearly the same results, as the proven questionnaire.

Internal validity. Internal validity is achieved if you can claim that the results that you achieved with your research can be attributed to the factors that you considered and not to other factors which you did not consider.

It is a measure of the inherent cause and effect relationship between the factors that you considered in your research.

For example, if you can prove that a certain symptom is an indication of only one specific illness, then your finding will have internal validity.

External validity. External validity relates to how you apply the results of your investigation to the wider population.

It tells you if your findings apply generally or only to the target group of your research.

For example, if you can prove that your findings, based on a sample taken from a certain population also apply to any other group from any other population, then your research findings will have external validity.

Calculating statistical significance

Statistical significance means that you are sure that the statistics that you generated are reliable.

It does not necessarily mean that your findings are important.

Statistical significance can, for example, be skewed by the size of the sample that you investigate.

The larger the sample, the more significant will small differences between two variables appear to be.

Analyzing statistics

There are many ways in which statistics can be analyzed.

Numbers as such seldom provide a clear picture of any value for coming to conclusions.

Dedicated computer software will mostly provide you with such numbers.

Ultimately, however, it is up to you to interpret the numbers and to make sense of them.

For this purpose, you might need to summarize the data or rearrange it in tabular or graphic format.

Some computer programmes might do this for you. They might even interpret the data to an extent, but they will not come to conclusions or findings.

You might, for example, need to group statistics in different age groups, gender, nominal ranges, etc. to see the bigger picture from which to come to conclusions.

This can be made visual in the forms of tables, line graphs, bar charts, histograms, etc.

The computer software might do some handy calculations for you, for example calculating averages, also called the mean; medians (the midpoint of the data); mode (most common value in a set of data); range (the difference between the smallest and the largest value); standard deviation (the average spread around the mean); variance (the square of the standard deviation), etc.

Coming to conclusions from statistical data

Statistics are often used as a basis for coming to conclusions about presumed effects and relationships.

There are several principles of statistics that, if violated, can affect the inferences made from results as well as subsequent conclusions of the research.

Sophisticated statistics do not guarantee valid conclusions.

You will, therefore, need to obtain the assistance of an expert statistician to help you interpret statistical data if you are not one.

However, coming to conclusions and developing findings from them are still your responsibility.

Summary

The internal validity of conclusions is tested against statistical and scientific laws.

There are different kinds of validities, depending on how and against what your conclusions are tested.

Kinds of validity include:

Construct validity.
Content validity.
Face validity.
Conclusion validity.
Criterion validity.
Internal validity.
External validity.

Statistical significance is achieved if your statistics are reliable.

Reliability is often damaged when the size or composition of your sample is wrong.

Statistics can be analyzed by consolidating them in a table or graphs.

Some analysis and calculations are often done by computer.

You will need to come to your own conclusions based on your interpretation of the data.

Finally, you will need to derive findings from your conclusions.

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ARTICLE 39: Research Methods for Ph. D. and Master’s Degree Studies: Statistical Research Methods Part 1 of 2.

6th Sep 2020 No Comments

Written by Dr Hannes Nel

Introduction

Technicist scientists are of the opinion that natural science is the most reliable path to the truth.

They, furthermore, claim that the truth can only be known through scientific proof.

Truth is based on logic, they say.

They believe in the singularity of meaning.

Something is either true or false – there is no in-between.

That is why they often base their research on hypotheses rather than a research question or statement.

They also believe that the truth can be proven and expressed numerically.

And they believe that the truth is not dependent on context or time.

Social scientists do not agree.

They feel that experience and reflection should not be neglected.

Individual and group perceptions can often be the truth.

The truth can be different in different contexts and at differ times.

Logic is simply common sense.

I will discuss the following issues related to statistical research methods in this article:

Investigating a statistical hypothesis.
Conducting statistical regression analysis.

Investigating a statistical hypothesis

You will mostly use a hypothesis in statistical research, although it is also possible to base your research on a problem statement or question.

You will need to formulate two opposing hypotheses – the null hypothesis and the alternative hypothesis.

The null hypothesis, indicated with H₀, (H-naught) is a statement about the population that you believe to be true.

The alternative hypothesis, indicated with H₁, is a claim about the population that is contradictory to H₀. It is what we will conclude when you reject H₀.

A null hypothesis can often be proved or disproved by means of statistical research.

One of your samples will support the H₀ hypothesis while the other will support the H₁ hypothesis.

You will reject the H₀ hypothesis if the sample information favours the H₁ hypothesis.

Or you will not reject the H₀ hypothesis if the sample information is insufficient to reject it.

For example, your H₀ hypothesis can be:

30% or less of the people who contracted the COVID-19 virus lived in rural areas.

You can also write the null hypothesis like this: H₀ ≤ .3

Your H₁ hypothesis will then be:

More than 30% of the people who contracted the COVID-19 virus did not live in rural areas.

You can also write the alternative hypothesis like this: N₁ > .3

You will also need to calculate the size of the sample that you should use with a certain accuracy probability.

Dedicated computer programmes will do this for you.

Once you have composed a sample that will give you some answers with an acceptable level or probability, you will need to interpret the data that was probably analyzed with dedicated software.

You will need to set certain norms, or criteria, for the analysis of the data that you collected for the population first.

The samples also need to meet those norms, criteria or parameters.

A null hypothesis needs to be proven by comparing two sets of data.

If you reject the null hypothesis, then we can assume that there is enough evidence to support the alternative hypothesis.

That is: More than 30% of the people who contracted the COVID-19 virus did not live in rural areas.

You will probably compare the mean of observations or responses for the two sets of data.

It might sometimes be necessary to use the mode, median or correlation between the sets of data.

Random variability between different samples will also always be present.

There might also be small differences between the statistical relationship in the sample and the population.

It is possible that this can be just a matter of sample error.

Dedicated computer software will do the statistical calculations for you.

A null hypothesis does not “prove” anything to be true, but rather that the hypothesis is false.

If you cannot prove the two phenomena or populations to be different, then they are probably the same.

Then again, if the statistical analysis does not enable you to reject the null hypothesis, it does not necessarily mean that the null hypothesis is true.

Conducting statistical regression

Statistical regression analysis is a generic term for all methods in which quantitative data is collected and interpreted to numerically express the relationship between two groups of variables.

The expression may be used to describe the relationship between the two groups of variables.

It can also be used to predict values, although one must be careful of trying to predict future trends based on statistical data.

The two data groups, popularly represented by X and Y, are compared numerically or graphically to identify a relationship between the items or groups of items X and Y.

You can mostly use such comparisons to determine trends and correlation between variables.

It might, for example, be possible to identify a correlation between the hours that a student spends studying and his or her eventual performance in the exam.

Correlation measures the strength of association between two variables and the direction of the relationship.

In terms of the strength of the relationship, the values of the correlation coefficient will always vary between +1 and -1.

A value of +1 indicates a perfect degree of association between the two variables.

That means that if one thing happens, then something else will also happen.

For example, if you cut your arm you will bleed.

A value of -1 indicates a negative relationship between two variables.

For example, the faster you drive, the less time will it take you to reach your destination.

For example, the decrease in the number of new individuals that test positive for the COVID-19 virus does not enable us to predict when the pandemic will come to an end.

You can, perhaps, argue that correlation enables you to predict what will happen to one variable if a second variable changes.

However, predicting that such change will take place is often difficult, if not impossible in social sciences.

You can predict with a good measure of accuracy what will happen if you add certain amounts of yeast to the dough for baking bread.

But you cannot always predict how the baker will respond if she or he serves you the bread and you criticize it.

The situation is different in exact sciences, such as chemistry, where the scientist can initiate the change and control the size, measure and frequency of change.

Summary

You will probably use two opposing hypotheses in statistical research.

The null hypothesis is a statement about a population that you believe to be true.

The alternative hypothesis should contradict the null hypothesis.

You will use two samples to prove or disprove your hypothesis.

The findings that you gather from your analysis of the samples should apply to the population as well.

There might, however, be a sample error of which you should take note.

Statistical regression analysis investigates the relationship between two sets of variables.

It can show a correlation between the sets of variables.

It can also sometimes be used to predict values.

I would rather call it “foresee” values, because prediction based on statistics can be risky.

Relationships can be compared numerically or graphically.

Correlation between two variables can be anything between +1 and -1.

A value of +1 would indicate a perfectly positive correlation.

A value of -1 would indicate a perfectly negative correlation.

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ARTICLE 38: Research Methods for Ph. D. and Master’s Degree Studies: Sampling Part 6 of 6

5th Sep 2020 No Comments

Written by Dr. Hannes Nel

Introduction

Some academics and other scientists are of the opinion that the COVID-19 tests can be inaccurate by as much as 30 percent.

And there are those who believe that the mortality rates due to COVID-19 in some countries are much higher than the reported figures.

Perhaps it is true that findings and statistics are sometimes deliberately manipulated.

Then again, imagine how near impossible it must be to conduct research on an issue that affects the entire world.

Researchers often have no other choice than to make use of sampling.

And sampling facilitates efficiency and viability, not validity and accuracy.

I will discuss typical case sampling, unique-case sampling and volunteer sampling in this article.

Typical-case sampling

You can use typical-case sampling when you need to collect data on general items.

A typical-case sample is composed by identifying and including people who can be regarded as typical for a community or phenomenon.

Such a sample is used to avoid information, or worse, research findings and recommendations being rejected because they have been obtained from suspect, perhaps even deviant, cases.

It can also be used to avoid using data or opinions that are politically laden or otherwise manipulated.

A typical case sample should allow you, as the researcher, to develop a profile of what would generally be agreed as being average or normal.

Typical-case samples are often useful when large communities and complex problems are investigated.

Such samples enable those who are not familiar with a community to gain an understanding of the nature of the community in a relatively short time.

Members of the community can often help you to select items for a sample by suggesting criteria for such samples.

An example of a typical-case sample is when you choose your sample from a middle-class suburb rather than from a poor or rich suburb if you wish to do research on the spending habits of a city.

The spending habits of the poor and the rich would probably not be typical for the community.

Of course, your sample will be more representative of the community if you were to include poor, middle class and rich people in your sample.

But then you would be using random sampling or systematic sampling.

Unique-case sampling

In unique-case sampling, you would identify and include cases that are rare, unique or unusual in terms of one or more characteristics.

Such cases might agree with typical cases in other respects.

An example of unique-case sampling can be if you were to do research on the genetic makeup of a nation or tribe that has not been affected by die COVID-19 virus, or has been affected markedly less that the average for other countries.

Volunteer sampling

As in the case of snowball sampling, you will need to take intentional steps to gain access to individuals who are difficult to establish contact with.

Also, as in the case of snowball sampling, you might need to rely on volunteers for your sample group.

Then again, most research rely on the co-operation of volunteers.

You would typically start by approaching family members, friends, friends of friends, etc.

You can also ask for volunteers by posting an advertisement in a newspaper, ask for help on social media, write letters to possible volunteers, visit managers of businesses and ask them for assistance, etc.

Making use of volunteers whom you do not know as your sample can be risky.

You often do not have any control over the validity and accuracy, authenticity or sincerity of their responses to questions or any other contributions to your research.

It will, furthermore, be rather difficult to claim that your findings apply generally if you do not know the motives or reasons why volunteers became involved in your research project.

Summary

Typical-case sampling can be used with good effect to avoid using subjective data. This is done by collecting data from a general population, items or phenomena.

Unique-case sampling is used to investigate rare, unique or unusual cases or phenomena.

In volunteer sampling people are asked to volunteer to be included in the sample.

Volunteers need to be screened to ensure that they are authentic and trustworthy.

This is my last video on sampling, Methods. Therefore, I guess it would be fitting if I were to summarise the links between the different types of sampling. Here it is:

Cluster sampling is a form of stage sampling.
Convenience sampling is a form of opportunistic sampling.
Convenience sampling, dimensional sampling, quota sampling, purposive sampling and snowball sampling can be conducted as non-probability sampling.
Extreme-case sampling is used in conjunction with most other types of sampling.
Matched sampling and stratified sampling use systematic sampling.
Multi-phase sampling is a form of stage sampling.
Purposive sampling is a variant of boosted sampling.
Reputational sampling and unique-case sampling are variants of extreme-case sampling.
Snowball sampling is a form of volunteer sampling.
Systematic sampling is a modified form of random sampling.
Theoretical sampling is a form of criterion sampling and dimensional sampling.
Time sampling includes instantaneous sampling, interval sampling and duration sampling.
Typical-case sampling is related to case-study sampling.
Typical-case sampling is the opposite of critical-case sampling.

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ARTICLE 37: Research Methods for Ph. D. and Master’s degree Studies: Sampling Part 5 of 6

4th Sep 2020 No Comments

Written by Dr. Hannes Nel

Introduction

On face value sampling seems like a simple job.

And so it mostly is.

However, if you choose the wrong sample or you choose the sample incorrectly, you can destroy the validity and accuracy of your research project.

And you might have wasted a good number of years on fruitless research.

Think carefully about the examples that I offer in this post, especially the ones on systematic sampling.

I will discuss:

Stratified sampling.
Systematic sampling.
Theoretical sampling.
Time sampling.

In this post.

Stratified sampling

Stratified sampling is used to ensure that the sample is representative of a population with multiple characteristics that are evenly distributed amongst the population.

The research population is divided into homogeneous groups, with each group containing subjects with similar characteristics.

Such homogeneous groups are often called ‘sub-units’ or ‘strata’.

Samples are selected by making use of random selection procedures such as systematic sampling or simple random sampling.

For example, students at a specific university, which are the population on which the research will be conducted, can be grouped into a male and a female group.

Or they can be grouped per faculty.

Or per leisure time interests, etc.

If, for example, you wish to do research on the impact of leisure time interest on academic performance, you will need to investigate a representative sample from each leisure time interest group.

Representivity is achieved by identifying the parameters of the wider population and taking them into consideration when composing samples.

So, in this example leisure time utility will be the independent variable.

Factors such as gender, age, occupation, academic year, etc. can be the dependent variables.

For the sake of coming to valid conclusions and findings, the process of organizing a stratified sample requires ensuring that the characteristics typical of the wider community are present in the sample.

If you draw more than one sample, you must also ensure that the samples are homogeneous in terms of at least one characteristic, which would be your independent variable.

In qualitative research, you will probably not calculate the size of the sample in terms of a statistical level of accuracy.

Therefore, representivity will depend on your own judgement.

You do need to take certain factors into consideration, though.

For example, the size of the population, time and cost constraints, access to data, the need for simplicity and the purpose of the reach.

Systematic sampling

Although some simple calculations need to be done with systematic sampling, it is not enough to be called quantitative research.

Systematic sampling is a modified form of random sampling.

For example, in a population of 10,000 individuals, you might feel that you should have a sample of, say, 200 people.

This will mean that you should select every first person from each sub-unit of 50 for your sample.

Fifty is, thus, your sample interval, i.e. the distance between each element selected for the sample.

You can choose numbers 1, 51, 101, 151, etc. for your sample.

If, for example, the first 57 people on the list that you use are the only females, you will have only two females in your sample.

This will probably distort your findings.

Another example of a skewed list would be if you work on a number of name lists for different faculties and the faculty lists are ordered normatively with the best performing student as the first name on the list and the poorest performing student as the last name on the list.

To use an extreme example, if there are fifty names on each list, your sample will include only the poorest performing students.

Periodicity can be a problem with systematic sampling if the list is not a fully random one.

For example, if you start by selecting the first name on the list, then names numbered 1 to 49, 50 to 99, 100 to 149, etc. do not have any chance of being selected for the sample.

You can eliminate this problem by ‘randomizing’ the list first by ‘shuffling’ the names like you would a deck of playing cards, and then selecting the sample.

You can also deviate somewhat from a systematic selection. A sampling procedure is not cast in concrete and you can adapt it to your research needs.

Just as long as it improves the randomness of your sample.

You can, for example, use systematic sampling coupled with the condition that both genders are fairly represented in the sample.

This can be achieved by splitting the name lists for males and females and then selecting a number of males and females from each list randomly.

Theoretical sampling

Theoretical sampling is the process of investigating incidents, events, occurrences or people over a period based on their potential to represent or demonstrate important theoretical constructs.

Researchers who follow an approach where deductions can be made from data with which theory can be developed or extended would be interested in finding individuals with the right makeup, or cases that embody theoretical constructs.

Theoretical sampling, therefore, is a special type of criterion sampling.

As the name implies, theoretical sampling is best used when the research focuses on theory and concept development.

Your goal would be to develop theory and concepts that are connected to, are grounded in, or emergent from real life events and circumstances.

To generate new theory will often require substantial research and is, therefore, a time-consuming process.

You will need to analyze and probably reconstruct and deconstruct existing theory until you manage to develop new theoretical ideas.

As opposed to purposeful sampling, you cannot know in advance precisely what to sample for and where it will lead you when you use theoretical sampling.

That is why theoretical sampling fits in well with grounded theory and why you will probably work towards solving a problem statement or question rather than hypothesis testing.

Time sampling

Time sampling is where observations of occurrences or events need to be taken and recorded at certain times.

You can use it if it is important to know the chronology of events.

Time sampling can be instantaneous, at specific intervals or measured in terms of how long it takes, i.e. duration.

Instantaneous sampling is achieved by observing an event or occurrence at standard intervals, for example every minute, hour, etc. on the dot.

You will need to take observations at a specific time and intervals that you planned on, or that are prescribed or necessary for whatever reason and you will take notes of your observations.

In the case of interval recording, you will observe and record events or occurrences during each interval.

This means that you will record observations during each interval for the entire time of the interval and not just at the moment each interval starts.

For example, you might wish to conduct research on the emotional state of a patient over a period and at set intervals, say every fifteen minutes for a day.

You can then count the number of times that the patient is happy, sad, angry, etc. and how the patient expressed the emotions.

The patient might have smiled, cried, laughed, etc.

You might also need to take note of what possibly might have triggered the emotion.

Duration sampling is where you will measure how long it takes for an individual or group to complete a certain task.

With duration sampling, you might, for example, need to record how long it takes the patient to overcome an anger attack or any other emotional state.

Or you might need to record how often the individual switches between different emotions, and many more.

The format of your notes will depend on the type of data that you wish to collect.

Time sampling will often require a quantitative research approach or at least some calculations.

This, however, does not mean that it cannot be used in qualitative research.

It might also be necessary to use a mixed approach, i.e. quantitative and qualitative research.

Summary

Stratified sampling is where you will select a representative sample from a diverse community. You will use random sampling to select the sample or samples.

In systematic sampling you will select individuals or items from a population at structured intervals.

In theoretical sampling you will select the sample based on certain criteria that will enable you to develop new theories and concepts.

Time sampling is where you will take samples at certain times. It can be instantaneous, at specific intervals or measured in terms of duration.

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ARTICLE 36: Research Methods for Ph. D. and Master’s Degree Studies: Sampling Part 4 of 6

2nd Sep 2020 No Comments

Written by Dr. Hannes Nel

Introduction

Sampling types mostly differ only in the way in which the sample is composed.

Ultimately, samples are all small extracts from a larger population.

They are studied because the entire population is too large for viable research.

Obviously, the sample should display behaviour, phenomena, events, etc. that would be typical for the entire population.

That means that the research findings based on the sample should be generalizable.

This, however, is not always the case.

Researchers sometimes limit their research to the sample without even trying to achieve generalizability.

In effect, what is supposed to be a sample becomes the population.

I will discuss the following sampling methods in this article:

Probability sampling.
Purposive sampling.
Quota sampling.
Random sampling.
Reputational-case sampling.
Snowball sampling.
Stage sampling.

Probability sampling

A probability sample is drawn randomly from the wider population.

Therefore, it will be useful if you need to generalize.

Or if you seek representativeness of the wider population.

The name already reveals that it should be used with quantitative research.

Obviously, statistical calculations will form part of the research process.

Probability or representativeness is calculated with a wonted measure of accuracy probability.

For example, 97% (giving an error factor of 3%).

The risk of bias is less than if you were to rely on your gut feeling or subjective judgement.

However, all samples, regardless of whether they are based on statistical calculation or your judgement, are hampered by a measure of sample error.

Purposive sampling

Purposive sampling is also sometimes called purposeful sampling or judgmental sampling.

In purposive sampling the researcher collects data according to the aims of the research.

To develop a purposive sample that will sufficiently represent the population:

You will need to know the profile of your target group.
And you will select items for the sample according to a list of important characteristics.

You can select purposive samples after you have studied the bigger population from which to select the sample.

This might require fieldwork or studying written profiles, such as curriculum vitae.

It can also require fieldwork and literature study.

You will need to find certain types of individuals displaying attributes that are needed for your research.

In horticultural research you will probably use categories such as resistance to plant diseases, flower colour, size and shape, etc.

In social research categories such as age, gender, status, role or function in organizations, stated philosophy or ideology, may serve as starting points.

For study in-depth, you will need to select information-rich cases.

As your research progresses, you may discover new categories which would lead you to more sampling in that particular dimension.

Quota sampling

For quota sampling you will need to choose representative individuals from a specific subgroup.

For example, numbers in accordance with the demographic composition of the total population.

You can simplify the process by first preparing a matrix table that creates cells or strata.

You may wish to use gender, age, education, or any other attributes to create and label each stratum or cell in the table.

The research question and the focus of your study will determine which attributes you should select for your sample.

You should use a nonprobability method to fill the cells.

Each category in the overall sample must be filled using the same recruitment procedure for the resulting groups to be comparable.

Next, you need to determine the proportion of each attribute in the full study population.

Let’s say you want to study perceptions of violence among people over age 50.

You can, for example, group the people in your sample as younger than 30; 30 to 39; 40 to 49; 50 to 59 and 60 and older.

You will need to determine the proportion of people in each age group, although it will often be best to have the same number of individuals in each group.

The groups younger than 50 are included for comparison purposes.

Random sampling

In random sampling, each possible sample has an equal probability of being chosen as the sample.

The sample needs to be large enough to deliver findings that will apply to the entire target group with a reasonable accuracy.

This depends on the size of the population and the measure of heterogeneity.

The larger the population, the larger the sample drawn should be.

A random sample is mostly used when each element of the population has the same chance of being selected to be part of the sample.

This is sometimes called ‘simple random sampling’.

The procedure used to draw the sample needs to ensure that as little bias as possible is present.

Drawing names from a hat, putting the names on a dart board and throwing darts at them to choose sample items, the roll of a dice are examples of how a random sample can be composed.

Some dedicated computer software can also select a random sample from a list of names.

Reputational-case sampling

Reputational-case sampling is a variant of extreme-case and unique-case sampling.

Like in the case of the extreme-case and unique-case sampling, you will choose a sample recommended by an expert in the field.

For example, you might be looking for individuals who have particular expertise that is most likely to advance your research interests.

Snowball sampling

Snowball sampling is also called chain referral sampling or respondent-driven sampling.

Snowball sampling is an effective way to locate subjects with certain attributes or characteristics necessary in the study.

Snowball samples are particularly popular among researchers who are interested in studying various classes of deviance.

Sensitive topics are often studied, and the sample often come from difficult-to-reach populations.

In snowball sampling, you would identify a small number of individuals who have the characteristics in which you are interested.

These people are then asked to identify and put you in touch with others who also have the wonted characteristics.

For example, if you are doing research on people who suffer from arachnophobia, you need to find only one person who is intensely scared of spiders and would be willing to put you in touch with others who suffer from arachnophobia to get the snowball rolling.

It so happens that this sampling method is especially useful for sampling a population where access and obtaining co-operation are difficult.

The basic procedure of snowball sampling begins by identifying one or more people with relevant characteristics and then interviewing them or asking them to complete a questionnaire.

After interviewing the subjects or after they have completed a questionnaire, you would ask them for the names of other people who possess the same attributes as them.

In this manner, a chain of subjects driven by the referral of one respondent to another is formed.

Stage sampling

Stage sampling is an extension of cluster sampling.

It involves selecting the sample in stages, i.e. taking samples of samples.

Doing research on the value systems of universities, you can first select a cluster of universities as your sample, then certain faculties in each university as a sub-sample, then a number of students from each faculty as your sub-sub sample.

Summary

A probability sample is a random sample for which the measure of probable accuracy is calculated.

In purposive sampling you would collect data based on the aim of your research. The characteristics of the population from which you will draw a sample will be taken into consideration.

A quota sample is drawn from a population that represents the profile of your research target. The profile is based on your research question and the focus of your study.

In random sampling each possible sample has an equal chance of being chosen for your research.

In reputational-case sampling you will choose a sample recommended by an expert in the field.

In snowball sampling you would identify a small sample or perhaps just one individual who meets the requirements for your research. This individual or small group can recommend other individuals or groups that meet your requirements.

Stage sampling is the selection of a sample in stages, that is taking samples from samples.

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ARTICLE 35: Research Methods for Ph. D. Studies: Sampling Part 3 of 6

1st Sep 2020 No Comments

Written by Dr. Hannes Nel

Introduction

I will discuss event sampling, extreme-case sampling, matched sampling, multi-phase sampling, non-probability sampling and opportunistic sampling in this article.

Event sampling

Of all the types of sampling, event sampling is the most a research method rather than a data collection method.

You would typically select a small group of individuals to investigate.

It requires counting the number of times that an occurrence is observed or a statement, word, etc. is found in a data source, for example a document.

Counting words, statements, etc. in a document is easy if it is available in electronic format.

An example of this is to count the number of times that the words “he” and “she” respectively are used in a book to determine if there is gender discrimination against one or the other.

You can use your laptop computer to count the words for you.

Any word processor on computer has the facility to count words.

When your research requires you to observe certain repetitive actions, you will need to develop statements or criteria for the action.

This can be compared to the cricket scorebooks that some clubs still use, although computer programmes for even that have been developed.

The task becomes more difficult if it is not only necessary to count the number of times actions are repeated, but also the chronological order in which the actions took place.

An example of this is where you need to determine what kind of response a certain action invites, such as how people respond to a smile, compliment or insult.

Extreme-case sampling

Extreme-case sampling is used when information about unusual cases that may be particularly troublesome, or enlightening are sought.

Such a sample might represent the purest instance of a phenomenon that you wish to investigate.

Obviously, such cases are likely to be exceptions to the rule.

You might identify and investigate extreme cases to develop a richer, more in-depth understanding of a phenomenon.

You can also use extreme-case sampling to lend credibility to your research project.

Extreme-case sampling is often used in conjunction with other sampling methods.

In such events the extreme-case will be investigated in the context of the other sampling method.

The extreme-case can be used as an outlier, that is an observation that takes on an extremely high or extremely low value, thereby strengthening the norm.

An extreme-case can also be investigated on its own.

For example, where you do research on a specific individual who is extremely gifted, rich, strong, etc.

Matched sampling

In matched sampling one member of a control group is matched to a member of an experimental group.

Matching is done randomly, but the independent variables that are considered important for the research are taken into consideration.

Pairs of participants are matched in terms of the independent variables.

For example, age, gender, academic qualifications, etc. and only then assigned to the control or experimental group.

Matching pairs are used mostly when experimental research methods are used.

This implies that it is more valuable to quantitative research than to qualitative research.

However, experimental research methods can be used with qualitative research methodology.

Therefore, matching pairs can also be used to compose samples for such research.

Multi-phase sampling

Multi-phase sampling is a form of stage sampling.

The difference between multi-phase sampling and stage sampling is this:

In the case of stage sampling the criteria on each level are pretty much the same for each level of sampling in a particular region or field.

You will take samples of samples.

For example, your initial sample can be 1000 students randomly selected at a university.

Your next level sample can be 500 students who enrolled for psychology.

Your third level can be the 100 students who achieve the highest marks in the final exam.

In multi-phase sampling the criteria change on each ensuing level.

For example, the first stage criterion might be region.

The second stage criterion can be students who excel in numeracy skills.

The third stage criterion can be students with blue eyes.

Non-probability sampling

Convenience sampling, quota sampling, dimensional sampling, purposive sampling and snowball sampling can all be conducted in a non-probability sampling manner.

In non-probability sampling you, as the researcher, select the sample based on your own subjective judgement.

Non-probability infers that randomness ins not required, and the accuracy of the research findings need not be accurate to a good measure of probability, for example 90%.

In non-probability sampling, you will do research on a specific group to obtain knowledge about the group.

You will not claim general applicability of your findings.

The group, therefore, is important rather than any wider population.

This is often the case with small-scale research.

For example, just two or three faculties in a university,

Or just the lecturers in a small number of faculties.

Small-scale research often uses non-probability samples.

Meaning that not all available individuals have an equal chance of being selected for the sample.

The more expertise you have of the field of study, the better will you be able to select your sample.

Such samples are far less complicated to set up than a randomly selected sample.

However, keep in mind that they probably do not represent a substantive population.

Then again, they are less expensive than random samples and can achieve the purpose of the research if the general applicability of the findings is not important.

Small-scale research can also be used to pilot data collection tools, such as questionnaires, before they are used in actual research.

Opportunistic sampling

Opportunistic sampling means taking advantage of unanticipated events, leads, ideas, hints, and issues.

Accidental sampling is similar, but slightly different, as we saw in my previous post on convenience sampling.

The sample is composed of items upon which you stumbled by chance.

People who are available at the time of your study can be included in the sample.

They will need to provide valuable information and they must fit the criteria that you need.

A friend, who unknowingly shares valuable information with you at a party can be included in your sample.

Opportunistic sampling can be risky because the data that you collect can often not be generalized.

It might, furthermore, be difficult to corroborate the information.

Your source might not be reputable and might not have any credentials or qualifications making him or her an authoritative or expert source.

Summary

Event sampling is where you would do research on one or a small number of people, occurrences, or phenomena.

Extreme-case sampling also focus on just one or a small number of people, occurrences, or phenomena. Only here you will look for an unusual case or cases.

In matched sampling members of a control group are compared in terms of independent variables to members of an experimental group.

In multi-phase sampling the sample is broken down in terms of different criteria for each phase or level.

Non-probability sampling is selecting a sample that does not necessarily represent the population.

The result of this would be that your research findings cannot be generalized.

Opportunistic sampling means using any data sources that you can find without deliberately selecting them.

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ARTICLE 34: Research Methods for Ph. D. Studies: Sampling Part 2 of 6

30th Aug 2020 No Comments

Written by Dr. Hannes Nel

Introduction

I discussed an introduction to sampling in my previous post.

I also discussed the first two types of sampling, namely boosted sampling and case study sampling.

To refresh your memory, boosted sampling is a type of sampling where you take specific steps to ensure that individuals who might otherwise have been omitted from the sample, are included.

Case study sampling is an investigation into a specific instance or phenomenon in its real context.

I will discuss cluster sampling, convenience sampling, critical-case sampling and dimensional sampling in this post.

Cluster sampling

A large and widely dispersed population brings with it, administrative problems.

Let’s say you want to investigate the impact of video games on teenagers.

It would be difficult to select and investigate a sample of, say, 1000 teenagers across the entire country.

You can reduce the time and work by selecting a smaller geographical area within the country.

This might have a negative effect on the generalizability of your findings.

It depends on your purpose with your research if this would be a problem or not.

But at least your research topic will now be viable.

This is an example of cluster sampling.

You can go one or more steps further by subdividing the geographical region into towns and towns into suburbs.

This is called ‘multi-stage cluster sampling’.

Limitations can be:

Younger teenagers will probably not be affected the same as older ones.
Teenagers in rural areas will not be affected the same as children living in urban areas.
There are many other possible variables that can have an impact on the results of the research.
For example, single-parent versus both parents in the family, personality traits, home conditions, etc.

The obvious risk with cluster sampling is that you can build in bias by excluding some possibilities.

The type and purpose of the research will determine if cluster sampling should be used or not.

Convenience sampling

Convenience sampling means selecting inputs and data from whoever happens to be available.

It is, thus, a rather opportunistic type of sampling.

It can also be accidental in nature, although there is a subtle difference between convenience sampling and opportunistic or accidental sampling.

Convenience sampling means making use of sources of information that you know of and that are easy to obtain.

Opportunistic or accidental samples are sources of information that you are not aware of in advance and that ‘falls into your lap’.

Convenience sampling is not a scientific way in which to collect data or to compose a sample.

It involves choosing the nearest individuals to serve as respondents.

It also means continuing the process until the required sample size has been reached.

Captive audiences such as students in a class are sometimes asked to discuss issues or complete questionnaires.

Convenience sampling is unlikely to deliver generally applicable findings.

Therefore, you will only use convenience sampling if achieving generalizable findings is not important to you and your research.

You must acknowledge that your findings are not applicable to a larger population than the small sample that you selected for your research.

It is even possible that your findings apply to your sample only.

Critical-case sampling

Critical-case sampling is sampling where it is important to obtain maximum applicability.

If the information and findings hold true for a critical case, it is likely to hold true for other cases and communities as well.

Critical cases are those that are likely to yield the most or most important information that will prove a hypothesis or solve a problem and that will have the greatest impact on the development of knowledge.

When selecting a critical-case sample, you would be looking for a ‘decisive’ case that would help you decide about which of several different explanations for a phenomenon, event or behavior is most plausible or most widely regarded as representing the general profile of a community.

For example, if one or a small number of people living in a jungle somewhere proves to have an immunity to the venom of a snake that can be found in that part of the world, one can probably deduce that there are people who have developed an immunity to the venom of that snake.

It does not necessarily mean that the tribe from which the sample was taken is immune to the venom of the snake.

This is a rather dramatic example and one will probably need to do more research and tests before you can claim with certainty that all people belonging to that tribe are immune to the venom.

It would also be interesting to do additional research on why the people are immune to the venom.

But please keep in mind that this example is a figment of my imagination – I don’t think there is such a tribe or snake.

Critical-case sampling is an efficient way in which to conduct research.

It need not be expensive because only one or a few items should be enough to prove your hypothesis or solve your research problem statement or question.

Dimensional sampling

Dimensional sampling is a refinement of quota sampling.

It can be used to reduce the sample size.

Dimensional sampling means selecting participants in the sample group in terms of a combination of criteria that you feel they should meet.

For example, when doing research on the correlation between perseverance and cognitive thinking ability, you can draw up a table with criteria for perseverance at the top (as column headings) and cognitive thinking ability down the side (as row headings).

A table like the one in the example can easily be converted into graphs of different types.

Summary

Cluster sampling is mostly used where the population is widely dispersed.

You will need to choose a cluster in the population that is representative of the population and that can realistically be investigated.

Convenience sampling means accepting any relevant data sources that you can easily find for your sample.

Convenience samples can be found by accident or coincidently.

Critical-case sampling focuses strongly on the purpose of your research.

The sample will often be too small to deliver generalizable findings.

Dimensional sampling is sampling where different characteristics of the sample are compared in the hope that the intersections of comparative data will deliver significant findings.

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ARTICLE 33: Research Methods for Ph. D. and Master’s Degree Studies: Sampling Part 1 of 6

29th Aug 2020 No Comments

Written by Dr. J.P. Nel

Introduction

I will discuss sampling in this and the five postings following on this one.

How large should your sample be if you were to do research on factors that make some people more susceptible to the COVID-19 virus than others?

Would you even use a sample, or would that be irresponsible for a topic that threatens human life as we know it?

Should one entrust an individual with such a critically important issue, or would it be something that should be done by a large team of researchers in as many countries as possible?

The three questions that I just asked should already show that sampling is not suitable for all research topics.

It is valuable for academic purposes and can be used if the main purpose is to broaden our knowledge.

As we all know, sampling is used to study the social and medical impact of the COVID-19 virus.

We also know that the findings of such research are sometimes questioned.

And we know that findings are sometimes proven wrong.

Sampling is largely about data collection.

However, it also includes the analysis of data.

That is why I am discussing it as a research method rather than a data collection method.

Obviously, sampling cannot be a stand-alone research method.

It must always be linked to other research methods.

The type and size of sample that you choose for your research can determine if your research will succeed or not.

You should choose the size and type of sample after you have chosen the target group for your research.

In quantitative research, you might need to calculate the size of the sample based on what percentage probability of accuracy you will need.

Dedicated computer programmes can often work out the sample size for you.

In qualitative research factors like expense, time available and where your target group is will determine the size of your sample.

Where the target group is, impacts on distance and accessibility, which will determine what size sample you will be able to reach and deal with.

The data collection method or methods that you will use will also have an impact on the size of your sample.

Although a sample should be large enough to provide valid and generally applicable information for a community, it should be small enough for you to manage.

Sampling in qualitative studies focuses on the quality of the information collected and not on the number of participants.

A sample of ten to twelve people in a community of 100 people is often acceptable.

Researchers in natural sciences will probably frown upon such a small sample or the unscientific way the sample size is decided upon.

Keep in mind that the response rate to questionnaires is often low.

You will do well if you achieve a 10% or more response rate.

If you need to receive at least 100 completed questionnaires back, you will need to send out at least 1,000 questionnaires.

To play safe I would send out double that number, i.e. 2,000 questionnaires.

Because if you don’t receive enough completed questionnaires you might need to send out more later.

You will not be able to receive as many responses through interviewing as you would through sending out questionnaires via the internet or the postal system.

Then again, you will not need to hold as many interviews as you would send out questionnaires.

Your sample must be representative of the population forming your target group.

Representativeness is determined by the size and composition of your sample.

A too-large sample is better than a too-small one.

You should, for example, not send your questionnaires only to people living in an old age home if you are doing research on people of all ages.

A random sample in terms of gender, age group, population group, intellectual capacity, interests and many more are often needed.

I will share 26 different types of sampling with you in this and five future articles.

Obviously, it would not be a good idea to discuss all of them in one post.

Therefore, I will spread them over six posts as shown on the slides.

Here, I will start with boosted sampling and case study sampling.

This article:

Introduction to sampling.
Boosted sampling.
Case study sampling.

Article 2:

Cluster sampling.
Convenience sampling.
Critical case sampling.
Dimensional sampling.

Article 3:

Event sampling.
Extreme case sampling.
Matched sampling.
Multi-purpose sampling.
Non-probability sampling.
Opportunistic sampling.

Article 4:

Probability sampling.
Purposive sampling.
Quota sampling.
Random sampling.
Reputational-case sampling.
Snowball sampling.
Stage sampling.

Article 5:

Stratified sampling.
Systematic sampling.
Theoretical sampling.
Time sampling.

Article 6:

Typical-case sampling.
Unique-case sampling.
Volunteer sampling.
Closing remarks.

Boosted sampling

Boosted sampling is a variant of purposive sampling.

It is a type of sampling where you take specific steps to ensure that certain individuals or types of individuals, who might otherwise have been omitted or underrepresented in the sample, are included.

People with special needs are often not included in samples because there are so few of them.

You can, for example, “boost” the sample by intentionally including people with special needs.

It is important to ensure that all relevant people are represented in the sample if you intend to do statistical analysis and quantitative research.

You might need the responses of specific people even if you are doing qualitative research.

Case study sampling

A case study is an investigation into a specific instance or phenomenon in its real context.

It is used to illustrate a general principle, pattern behavior, etc.

Case studies can establish cause and effect in a real context.

The value of a case study is largely dependent on the size and composition of the sample.

The advantage of a case study is that it serves as a small sample of a large whole, which makes it much more manageable.

This, of course, will only be so if the case being investigated is representative of the entire population being investigated.

It is important to allow case study events to speak for themselves rather than to depend too much on your interpretation, evaluation and judgement.

Data should be collected systematically and rigorously.

This means that you need to prepare well for case study research.

You should never manipulate a case because that will lead to false information and conclusions.

It is, however, not wrong to select a case as your sample to fit the purpose of your research.

For example, it would not be wrong to select tramps in an area frequented by them if you are doing research on factors that make people decide to turn their backs on society.

Summary

Sampling includes data collection and analysis.

It is always used in combination with other research methods.

The size of the sample will be statistically calculated in quantitative research.

Factors like time, funds, data collection methods, the purpose and topic of the research will decide the size of the sample in qualitative research.

The sample must be representative of the population for your research.

In boosted sampling you will take deliberate steps to ensure that certain elements in the population are included in the sample.

A case study sample will focus on a specific group or phenomenon.

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ARTICLE 32: Research Methods for Ph. D. and Master’s Degree Studies: Literature Study

27th Aug 2020 No Comments

Written by Dr. Hannes Nel

Introduction

People who do not like reading will probably shy away from making use of literature study for a Ph. D. or master’s degree.

I can understand such an attitude, especially if you don’t have any specific questions that you need answers to.

Or an academic problem to solve.

For some, there are many more exciting things to do rather than to read a book.

I guess studying late at night, over weekends, public holidays and university holidays is not something to look forward to.

Perhaps it takes a special kind of person, or some alien external force to motivate “normal” people to spend what they regard as leisure time engrossed in books.

However, if you embark on Ph. D. or master’s degree studies you will need to sacrifice some of your social freedom.

That does not mean that you will need to live like a recluse.

It only means that you will need to read a lot.

The point is this – as an adult, you are the captain of your ship.

Only you can decide what you should do with your life.

You need to be absolutely motivated to study for a Ph. D. or master’s degree.

So, let’s discuss literature study.

Literature study

Literature study will form part of most research work, regardless of what main research methods are used.

With the expansion of online data sources, it is becoming progressively more possible to undertake research without leaving your study or office.

You can even do research while having something to eat and drink in a restaurant or a bar.

Texts and records can be researched in four distinct ways:

The study of content.
The social construction of documents and records.
Documents ‘in the field’
Documents in action and documents in networks.

However, doing all your research by studying documents is deskwork rather than fieldwork.

When documents are included in the dataset, they tend to serve as ‘background material’ for many research projects.

Literature is often used to crosscheck oral accounts.

The empirical opportunities to analyze documents are endless: newspaper articles, advertisements, policy documents, government reports, blogs and web sites, schedules, letters, posters, pamphlets, brochures, campaign material, etc.

Everyday life offers a range of situations that involve forms and documents.

Particularly regarding interpersonal encounters within various institutions.

Even so, researchers interested in identifying practical examples may find it hard to recognize relevant events in a pile of documents.

The majority view of documentary data in qualitative research is that documents are detached from social action.

In contrast to an interview, the document appears more stable and fixed, whereas the content of an interview seems more dynamic and alive.

Documents can be quite lively agents in their own right rather than merely containers of text.

They can tell people what to do.

They can stir up conflicts.

They can evoke emotions such as anger, relief, envy, pride and despair.

Additionally, people do things with documents.

They can use them for various purposes, both intended or unintended.

They exchange documents.

They hide documents.

They write books and make movies about documents.

To recognize the aspects of documentary data, fieldwork rather than deskwork is required.

Summary

All researchers must do some literature study, regardless of which research approach or method they mainly use.

Texts and records are studied for the content, social construction, corroboration of other research methods and to support action research.

Literature study mostly means reading and analyzing books and other documents.

It can also include doing research on the internet.

Documents often trigger chains of interaction far beyond the original piece of paper.

Literature is often used to confirm research through other research methods.

Some researchers would rather do without literature study.

They prefer practical fieldwork or research in a laboratory that is not contaminated by old data.

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ARTICLE 31: Research Methods for Ph. D. and Master’s Degree Studies: Historical Research

27th Aug 2020 No Comments

Written by Dr. Hannes Nel

Introduction

Historical research can be conducted with the aim of answering a wide range of social research questions.

It is a systematic process of describing; analyzing and interpreting; and comparing the past.

The past can, of course, also be compared to the present.

It is based on information from selected sources as they relate to the topic under study.

Descriptive research

When conducted with a description in mind, historical research attempts to construct a map of the past.

It can also describe a developmental trajectory of events, for example, an educational system, political developments, community growth or deterioration, etc.

It involves locating events in time and place and requires sensitivity towards understanding the context within which an event took place or developed over time. Trajectories of development are plotted, and it may or may not try to explain how or why events occurred.

Historical research used for descriptive purposes also establishes background information about events.

Analytical and critical research

In analytical research, relationships between factors or events are critically interrogated within the context in which they occurred with the aim of exploring the possible causes and impact of the factors or events.

It requires critical, analytical scrutiny of documents and a process of cross-checking records and reports about incidents.

It aims to impact decision-making and policy formulation.

When conducting historical research, you might need to search for successes or mistakes from the past in order for a society or even an individual to avoid repeating mistakes made by others and to capitalize on the successes of the more fortunate or wiser.

The process of analytical research is complicated by the fact that there is seldom just one cause of an event.

You can never be certain if you did not omit the consideration of other important factors or events.

All sources of information should, therefore, be subjected to evaluation through processes known as external and internal criticism.

External criticism refers to the authenticity of the information.

For example, is the document that you are evaluating real or fake?

Internal criticism refers to whether the information is credible.

You need to determine if the information is consistent and accurate.

Rigour and sound analytical critique of sources lend considerable validity and reliability to the findings and conclusions reached.

Inferences about intent, motive and character are common, with the understanding of appropriateness to the context of the period.

Comparative research

Comparative historical research is much wider in scope than other historical research designs because the units of analysis are often whole societies or systems within societies.

It implies systematic research for similarities and differences between the cases under consideration.

Comparative researchers usually base their research on secondary sources, such as policy papers, historical documents, official statistics, etc.

Some degree of interviewing and observation can also be involved.

Historical comparative researchers generally prefer first-hand accounts, written by people who witnessed something personally, rather than documents derived from other secondary sources.

These researchers need to verify two important aspects regarding documents:

The validity of the documents’ content and its authenticity.

The content of a document is valid when it is not distorted, exaggerated or false.

Validity can be checked by making use of triangulation or any other form of corroboration.

Additional sources of information can be other, similar books, alternative documents, certification, living witnesses, demonstrations by the individual who claims authenticity, traces of validating substances, etc.

Authenticity refers to whether a document is a forgery.

Historical research can adopt paradigmatic approaches such as constructivism, critical race theory, empiricism and post-colonialism.

Sources of data

Broadly speaking there are four types of historical evidence that you can use – primary sources, secondary sources, running records and recollections.

Customarily, researchers rely on primary sources.

That is, the original source texts also called archival data.

Archival data are mostly kept in museums, archives, libraries or private collections.

Emphasis is given to the written word on paper, although modern histiography can involve any medium.

Substantial historical data is already captured electronically.

The internet is already a popular source of information, even though authenticity and accuracy are difficult to confirm.

Secondary sources are the work of other researchers writing about the issue being studied.

In its widest sense, a document simply means anything that contains text.

Official reports, records from schools, hospitals and courts of law, films, photographs, reports from journals, magazines, newspapers, letters, diaries, emails, and even graffiti scrawled on a wall are all examples of documents.

Running records are documentaries maintained by organizations.

For example, minutes of meetings, records of events, commentaries about events, war diaries, etc.

Recollections include autobiographies, memoirs, and oral relay of historical information.

Summary

Historical research answers a wide range of social questions.

It can be used to describe, analyse or interpret the past.

People can learn from historical events if it is accurately and objectively communicated.

Both mistakes and successes from the past can provide lessons to learn.

Analytical research attempts to provide the basis for understanding the past by exploring past events and trends and applying these to current events and trends.

Analytical research is complicated by the fact that successes and mistakes are mostly attributable to many variables.

Accuracy, authenticity and validity of data can be achieved through external and internal criticism.

Historical research makes use of four types of evidence – primary sources, secondary sources, running records and recollections.

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