A statistical range calculated around a sample statistic designed to contain the true population parameter a specified percentage of the time, most commonly $$95\%$$. Some researchers advocate using confidence intervals as an alternative to traditional null hypothesis testing because they are often more intuitive to interpret. Furthermore, a confidence interval inherently provides the data needed to perform a null hypothesis test; if a hypothetical population mean falls completely outside the calculated interval, the sample mean is considered statistically significantly different from that hypothetical value.

Confidence Interval

In survey research, a sample of about $$1,000$$ individuals is typically considered adequate to make accurate estimates, regardless of whether the broader population consists of a hundred thousand or a hundred million people. This is because a $$95\%$$ confidence interval depends only on the size of the sample itself, not on the size of the population. Furthermore, while increasing the sample size continues to shrink the confidence interval—meaning the sample statistic is likely closer to the true population value—it does so at a progressively slower rate. Consequently, the minor gains in statistical confidence achieved by surveying significantly more than $$1,000$$ people are generally not considered worth the additional time and financial cost.

Sample Size and Population Size

When determining the optimal sample size for a survey, what are the two primary factors a researcher must generally balance?

The optimal sample size for a survey generally depends on two primary factors: the researcher's desired level of statistical confidence and the practical constraints of the study's budget. While larger samples yield statistics that are closer to the true population value and provide greater confidence, they also require more time, effort, and money to collect. Researchers frequently use power analyses to balance these theoretical and practical considerations.

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A sample is a smaller subset of individuals selected from a larger population of interest. Because it is usually impossible to study every member of a population, researchers measure variables within a sample with the intention of generalizing their findings back to the broader group, ideally using a representative sample that closely resembles the population.

Sample

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KPU Research Methods in Psychology - 4th American Edition

In research, the sample is studied with the goal of generalizing the results to the broader population from which the sample was drawn. This process allows researchers to make inferences about a large group based on data collected from a smaller, representative subset. The relationship is visually comparable to extracting a small representative group from a vast crowd.

Relationship Between Sample and Population

A team of researchers wants to understand the typical sleep habits of all adults in a country of 50 million people. Since they cannot survey every individual, which of the following approaches would be the most practical and scientifically sound first step for their investigation?

A random sample is a subset of a larger population in which every member of the population has an equal chance of being selected. This method is often preferred for selecting experimental participants because, provided the sample is large enough, it provides reasonable assurance that the participating individuals are representative of the broader population.

Random Sample

To illustrate how a sample is used, a researcher might measure the talkativeness of a few hundred university students. This subset serves as the sample, which the researcher studies with the intention of drawing conclusions about the talkativeness of a much larger population, such as men and women in general.

Example of a Sample: Talkativeness Study

A representative sample is a study sample that is similar to the broader population in important respects. It is crucial for researchers to obtain a representative sample so they can appropriately generalize their findings from the small subset of participants to the entire population of interest.

Representative Sample

Inferential statistics are a set of mathematical techniques used by researchers to determine whether a statistical result or relationship observed in a study's sample reflects something that is genuinely true of the broader population.

Inferential Statistics

Probability sampling is a broad category of sampling methods where the researcher can mathematically specify the exact probability that each member of the defined population will be selected for the sample. Because it enables researchers to make highly accurate estimates about a population, it is the favored approach in survey research, though it requires a clear and precise specification of the target population before sampling begins.

Probability Sampling

Non-probability sampling encompasses methods where the researcher cannot mathematically specify the probability that any given member of the target population will be selected for the sample. Because it does not rely on structured random selection from a clearly defined population, it is the most common approach used in general psychological research, even though it limits the ability to make perfectly representative population estimates.

Non-probability Sampling

Determinants of Survey Sample Size

Convenience sampling is a common form of non-probability sampling where researchers study individuals who happen to be physically nearby and are readily willing to participate, such as college students in an introductory psychology course. While this approach is frequently used in psychological research due to its accessibility and efficiency, its main disadvantage is that the resulting sample may not accurately represent the broader population, severely limiting the ability to generalize the findings.

Convenience Sampling

A survey non-responder is an individual selected for a survey sample who fails to complete the questionnaire. This lack of participation can occur for various reasons, including moving away, being too busy, lacking interest in the topic, or refusing to participate on principle.

Survey Non-responder

Simple random sampling is a method for obtaining a study sample where every single member of the target population has an equal chance of being selected. While this approach is effective for ensuring a representative sample, it is often difficult or impossible to achieve in psychological research because populations are rarely defined clearly enough to give everyone an equal selection chance.

Simple Random Sampling

Sampling bias is a systematic error that occurs when the method used to select participants results in a sample that fails to accurately represent the broader target population. Because the selected individuals differ in important ways from the overall group, any statistical findings derived from this unrepresentative sample will likely be inaccurate and cannot be safely generalized.

Sampling Bias

Measures of central tendency are descriptive statistics used to describe the typical, average, or center scores within a distribution. Common examples of these measures include the mean, median, and mode.

Measures of Central Tendency

To conduct a study, researchers typically select a smaller subset of individuals from a broader group of interest. This smaller subset is referred to as a ____.

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