Samples and Populations, Explained

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Samples and Populations

Research Methods in Psychology · Chapter 3: Research Design and Methodological PlanningSection 3.6 · lesson 21 of 9411 min · free with a free account

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In this lesson

Understanding sampling theory and its implications for generalizing research findings.

  • Define population, sample and representativeness
  • Distinguish probability from non-probability sampling
  • Explain sampling error and statistical power
  • Judge whether a sample supports its conclusion

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Transcript

Everything said in the video, section by section (1,442 words). Read along, or search it.

Research Design and Methodological Planning

Samples and Populations

Research questions in psychology are posed about enormous groups of people. All adults. All adolescents in India. Everyone diagnosed with a particular disorder. Studies are run on a few dozen, or a few hundred. The whole logic of scientific inference lives in that gap. This section is about when you are allowed to cross it, and when you are not. By the end you will define population, sample, and representativeness precisely. You will distinguish probability sampling from non-probability sampling. You will explain sampling error, and why sample size drives statistical power. And you will meet the single most quoted sampling problem in modern psychology. It has an acronym, and the acronym is not flattering.

Why Sampling Matters

Studying Few, Claiming Many

Start with why any of this matters. A sample that accurately represents its population lets you generalize. You can apply the finding to the broader group with some confidence. A sample that does not represent its population still produces a finding. But the reach of that finding is limited to people resembling the sample itself. Which is usually a far smaller claim than the researcher wanted to make. Now here is the part worth memorizing. The most sophisticated statistical analysis cannot compensate for an unrepresentative sample. The damage happens before the analysis begins, when you decide who gets recruited. So sampling is not an administrative detail at the start of a study. It is the decision that fixes what your results can mean.

Two Groups

Population, Sample, Representativeness

Two terms, and one relationship between them. A population is the entire group of individuals to whom you intend the findings to apply. Populations may be very large, such as all adults in India. Or relatively focused, such as all final-year medical students at universities in Maharashtra. The population must be defined before sampling begins, not afterward. A sample is the subset of that population from whom data are actually collected. Researchers work with samples for practical reasons. Cost, time, and access. But the goal is always to draw conclusions that extend beyond the sample. And that extension is only justified when the sample is representative. A representative sample mirrors the population on characteristics relevant to the question. A biased sample systematically over-represents or under-represents parts of the population.

Known Chances

Probability Sampling

Sampling methods divide into two families, and the divide is sharper than it looks. In probability sampling, every member of the population has a known chance of selection. Known, and non-zero. Both halves of that matter. That single property is what unlocks everything else. It makes it possible to calculate the sampling error. And it makes statistically valid inference about the population defensible. There are four probability methods in common use. Simple random sampling, systematic sampling, stratified random sampling, and cluster sampling. They are not competing theories. Each one solves a different practical obstacle to selecting people at random.

Four Methods

Choosing a Probability Method

In simple random sampling, every member has an equal probability of selection. You use a random number generator, or a lottery method. It works when a complete list of the population exists, and the population is fairly homogeneous. Systematic sampling selects every nth member of a list. Every tenth name in a database, for example. Use it when a comprehensive ordered list exists, and full randomizing is impractical. Stratified random sampling divides the population into subgroups, called strata. Random samples are then drawn from each stratum, in proportion to its size. Use it when key subgroups must be adequately represented, such as age groups. Cluster sampling randomly selects naturally occurring groups instead of individuals. Schools, or hospitals, when the population is geographically dispersed.

Unknown Chances

Non-Probability Sampling

Now the other family. In non-probability sampling, not all members have a known chance of being selected. These methods are often more practical, and considerably less costly. They also carry a much greater risk of selection bias. Which limits how far the findings can honestly be generalized. Convenience sampling recruits whoever is most easily accessible. Psychology students from the researcher's own university, most famously. Purposive sampling deliberately selects participants who meet specific criteria. Criteria relevant to the research question, chosen by the researcher. You cannot calculate a sampling error from a purposive sample. Representativeness then rests entirely on the researcher's judgment, which a reader cannot check.

Practical But Riskier

Four Non-Probability Methods

Two more non-probability methods are worth knowing by name. Snowball sampling has existing participants recruit new ones from their own networks. It is the practical choice for hard-to-reach populations. The price is that the sample may cluster around social networks. So it may not represent the full population at all. Quota sampling recruits until pre-specified quotas for key demographic groups are filled. That sounds like stratified sampling, and it is not. There is no random selection within the quotas. So you still cannot estimate the sampling error. Read the whole family this way. Each method buys practicality with a specific, named loss.

Natural Variability

Sampling Error

Now a term that sounds like a mistake and is not one. Sampling error is the natural variability that occurs when a sample is drawn from a population. Even with perfect random sampling, your sample statistic will not match the population exactly. That is not carelessness. It is arithmetic. And there is one lever that moves it. Larger samples produce smaller sampling errors. Their statistics are more reliable estimates of the true population values. Notice what sampling error is not. It is not bias. Bias pushes your estimate in one direction, consistently. Sampling error scatters it around the truth, which is why it can be calculated rather than removed.

Detecting Real Effects

Statistical Power

Sample size does more than shrink your error. It decides whether you could have detected the effect at all. Statistical power is the probability of detecting a true effect. Of correctly rejecting the null hypothesis, when the null hypothesis is false. Power depends on three things. The size of the effect being studied. A small effect is simply harder to see. The alpha level, typically point oh five. And the sample size. Small samples have low power, and the consequence is specific. They are likely to miss real effects, producing false negatives. A conclusion of nothing here, when there was something there all along. So researchers run a power analysis first, to find the minimum sample size needed to detect the expected effect. Conventionally, that means power of at least point eight zero.

Sizing A Study

What Drives Sample Size

Five factors drive how many participants you actually need. Effect size comes first. Smaller expected effects require larger samples to detect reliably. The alpha level is second. A more stringent alpha, point oh one rather than point oh five, requires a larger sample. Desired power is third. Asking for point nine zero rather than point eight zero costs participants. Design complexity is fourth. Factorial designs, and studies with multiple outcomes, both require larger samples. And attrition is fifth. Longitudinal studies must account for expected dropout by increasing the initial sample. Now the timing rule that all of this depends on. Sample size must be determined through power analysis before data collection begins. Run it afterward, and it is no longer a decision. It is a description of what you happen to have.

The WEIRD Problem

Whose Psychology Is It

Finally, the most cited sampling problem in modern psychology. A landmark analysis by Henrich, Heine, and Norenzayan, published in twenty ten. They found that roughly ninety-six percent of participants in leading psychology journals came from one kind of society. Western, Educated, Industrialized, Rich, and Democratic. Take the first letters, and you get the acronym WEIRD. Those societies represent only about twelve percent of the world's population. Many foundational findings may simply not generalize to the majority of human beings. The critique has changed practice. Psychology has invested in cross-cultural replication, and in more culturally diverse research teams. And it has grown more cautious about claiming that any finding applies universally. For researchers in India and other non-Western contexts, there is a direct implication. Locally normed measures and regionally relevant research are not a local interest. They are a scientific necessity.

Putting It Together

Summary, and One Test Case

Pull the section together. The relationship between samples and populations is central to scientific inference. Probability methods allow statistically valid generalization to a population. Non-probability methods are often more practical, and carry greater risks of bias. Sample size must be settled by power analysis, before data collection begins. And the WEIRD problem shows what systematic sampling bias costs an entire field. Now test yourself on one. Why would a study with twenty participants and a small expected effect produce unreliable findings? Answer it before you hear the answer. Power depends on effect size and sample size together, not on either one alone. A small effect in a small sample gives you very low power. So a real effect will probably go undetected, and the study will report nothing when there was something.

About Research Methods in Psychology at UPI Study

Research Methods in Psychology (Psychology 111) is a self-paced online course of 94 video lessons in 16 chapters, from the scientific method and research ethics to designs, data collection, sampling, measurement, validity, experiments, descriptive statistics and hypothesis testing. It carries a NCCRS credit recommendation for 3 semester credits.

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Universities that work with NCCRS

Research Methods in Psychology carries a NCCRS credit recommendation. These universities work with NCCRS; some are UPI Study's signed partners. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.

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FAQ

Questions students ask us

About Samples and Populations

What is the difference between a population and a sample in psychology research?
A population is the entire group a researcher wants the findings to apply to, such as all final-year medical students in Maharashtra, while a sample is the subset from whom data are actually collected. Researchers use samples because of cost, time and access. Findings can be generalized with confidence when the sample is representative, mirroring the population on relevant characteristics; no statistical analysis can fix an unrepresentative sample.
What is the difference between probability and non-probability sampling?
In probability sampling, every member of the population has a known, non-zero chance of selection, which allows sampling error to be calculated; methods include simple random, systematic, stratified and cluster sampling. In non-probability sampling, such as convenience, purposive, snowball and quota sampling, that chance is unknown. Non-probability methods are cheaper and more practical but carry a greater risk of selection bias, limiting generalization.
What is the WEIRD problem in psychology?
The WEIRD problem is the over-reliance of psychology on participants from Western, Educated, Industrialized, Rich and Democratic societies. In a 2010 paper, Joseph Henrich, Steven Heine and Ara Norenzayan highlighted that about 96% of participants in leading psychology journals came from such societies, which hold only about 12% of the world's population. Many findings may therefore not generalize, prompting more cross-cultural replication and caution about universal claims.
What is statistical power and how does sample size affect it?
Statistical power is the probability of detecting a true effect, that is, correctly rejecting a false null hypothesis. It depends on effect size, the alpha level (usually .05) and sample size. Small samples have low power and tend to miss real effects, producing false negatives. Researchers therefore run a power analysis before collecting data to find the minimum sample needed, conventionally for power of at least .80.

About the Research Methods in Psychology course

How many college credits is Research Methods in Psychology?
Research Methods in Psychology (Psychology 111) carries a NCCRS credit recommendation for 3 semester credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
How much does Research Methods in Psychology cost and what is included?
$250, paid once, with lifetime access: all 94 video lessons, a practice quiz after each, the graded work and final exam, and an official transcript when you finish. Students who want several courses choose UPI Study PRO instead.
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