Power Analysis and Measurement Validity in Social Research

What is the purpose of power analysis in research?

To determine sample size for detecting effects and to evaluate completed research for potential undetected effects.

What are the two major purposes of power analysis?

1. Planning research to determine sample size. 2. Evaluating completed research to assess if an effect was missed due to sample size.

What does statistical power indicate?

The probability of rejecting the null hypothesis when it is false.

What are the two decisions made during hypothesis testing?

1. Reject the null hypothesis (Ho) if the obtained value is larger than the critical value. 2. Fail to reject Ho if the observed value is smaller than the critical value.

What is a Type I error?

Occurs when we believe there is a genuine effect in the population when there isn't; probability is the α-level.

What is a Type II error?

Occurs when we believe there is no effect in the population when there is; probability is the β-level.

What is the relationship between Type I and Type II errors?

Hypothesis testing is a trade-off between the probabilities of the two competing types of error.

What does 1 - β represent in hypothesis testing?

The probability of rejecting Ho when it is false, or the statistical power of the study.

What three parameters affect the power of a statistical test?

1. Significance criterion (α). 2. Reliability of sample results. 3. Effect size (degree to which the phenomenon exists).

What factors can be estimated to determine statistical power?

1. Anticipated effect size. 2. Type of statistical analysis. 3. Selected α level. 4. Number of participants.

How is power determined as a function of α, effect size, and sample size?

Given specifications of α, effect size, and sample size, power can be calculated.

What is the acceptable standard of power in research?

A power of .80 is typically considered acceptable.

How is sample size specifically determined based on effect size, α, and power?

By specifying the desired power and effect size, the necessary sample size can be calculated.

What is the significance criterion (α) in hypothesis testing?

The threshold for determining whether to reject the null hypothesis, commonly set at 0.05.

What impact does a more liberal α-level have on statistical power?

Statistical power increases with a more liberal α-level.

How does sample size affect statistical power?

Larger sample sizes generally lead to greater statistical power.

What is the effect of using parametric tests on statistical power?

Parametric tests, which make stricter assumptions, tend to be more powerful than non-parametric tests.

What role do covariates play in increasing statistical power?

Including reliably measured covariates that are related to the outcome can increase the proportion of outcome variation predicted.

How does the reliability of outcome measures affect statistical power?

Less reliable measures obscure true signals, making it harder to detect treatment effects.

What is the difference between one-tailed and two-tailed tests in terms of power?

One-tailed tests are more powerful than two-tailed tests, which are more commonly used.

What is the relationship between effect size and statistical power?

All else being equal, larger effect sizes lead to greater statistical power.

What is the typical α-level used in hypothesis testing?

Commonly set at 0.05, but can also be 0.01 or 0.001.

What is the power of a test if the sample size is 30 and the effect size is a population r of .40 at α = .05?

Power equals .61, but researchers aim for .80.

What is the detectable effect size if power is .80 with α = .05 and n = 30?

The population r must be approximately .48.

What significance level must be used to detect a given effect size with specified power for a fixed sample size?

This type of analysis is uncommon due to conventions around significance levels.

What is the main goal of statistical power analysis?

To determine the sample size needed to achieve desired power levels for detecting effects.

What is the relationship between the four parameters of statistical inference?

Power, significance criterion (α), sample size (n), and effect size (ES) are interrelated; fixing three determines the fourth.

What is measurement in research?

The process of observing and recording observations collected as part of a research effort.

What are the key aspects of validity in measurement?

Validity refers to the accuracy of measurement and has six important aspects including evidence inference, dependence on various evidence types, expression by degree, inferences drawn from scores, being a unitary construct, and having multiple categories.

What is construct validity?

Construct validity addresses how confident we can be that a measure indicates a person's true score on a hypothetical construct or trait.

What is the definitionalist perspective on construct validity?

It holds that ensuring construct validity requires defining the construct so precisely that it can be operationalized straightforwardly.

What is the relationalist perspective on construct validity?

It suggests that concepts are related to each other, and the meaning of terms or constructs differs relatively rather than absolutely.

What are the two major categories of evidence for construct validity?

Translation Validity and Criterion-related Validity.

What is face validity?

The lowest level of validity where the operationalization seems like a good translation of the construct based on subjective judgment.

What is content validity?

It demonstrates that the content of a measure adequately assesses all aspects of the construct being measured.

What is predictive validity?

It assesses the operationalization's ability to predict something it should theoretically be able to predict.

What is concurrent validity?

It assesses the operationalization's ability to distinguish between groups that it should theoretically be able to distinguish.

What is convergent validity?

The extent to which evidence converges to indicate the degree of validity of a measure.

What is discriminant validity?

Evidence that a measure is not assessing something it is not supposed to measure, evaluated by its correlation with irrelevant variables.

What is the relationship between convergent and discriminant validity?

Both must be demonstrated to establish construct validity; they show related constructs are observed to be related and unrelated constructs are not.

What are some threats to construct validity?

Inadequate preoperational explication, mono-operation bias, mono-method bias, interaction of different treatments, and social threats like hypothesis guessing.

What is reliability in measurement?

The consistency or repeatability of measures, indicating the degree to which a test consistently measures what it is supposed to measure.

What is true score theory?

It maintains that every measurement is a composite of true ability and random error, expressed as X = T + e.

What does var(X) = var(T) + var(e) signify?

It indicates that the variability of a measure is the sum of the variability due to true score and the variability due to random error.

Why is it important to consider random error in measurement?

It reminds us that most measurement has an error component and is foundational to reliability theory.

What is the goal of having reliable measures?

To show little change over time, assuming that the traits measured are stable.

What is the significance of validity in research?

Validity ensures that the conclusions drawn from research findings accurately reflect the constructs being measured.

How can validity be expressed?

Validity can be expressed by degree, such as high, moderate, or low.

What does it mean for validity to be a unitary construct?

It means validity is a single concept that encompasses various categories of evidence supporting or opposing a measure's validity.

What is the role of operationalization in construct validity?

Operationalization must accurately reflect the theoretical constructs to ensure valid inferences can be made.

What is the importance of assessing the content of a measure?

It ensures that the measure is relevant and representative of the construct it aims to assess.

What is the impact of unclear test directions on construct validity?

It can lead to confusion and misinterpretation, negatively affecting the validity of the measurement.

What are some common issues that threaten construct validity?

Confusing test items, overly complex vocabulary, and inconsistent scoring methods can all threaten construct validity.

What is a measure with perfect reliability?

A measure that has no random error and is all true score.

What is the reliability of a measure that has only random error?

It has zero reliability.

What are the two types of measurement error?

Random error and systematic error.

What causes random error?

Factors that randomly affect measurement of the variable across the sample, such as mood.

What is systematic error?

Factors that systematically affect measurement of the variable across the sample, such as noise from traffic affecting test scores.

How can measurement error be reduced?

By pilot testing instruments, training interviewers, double-checking data, using statistical adjustments, and employing multiple measures.

What does reliability refer to?

Consistency of a measure, which can be assessed across time, forms, and items.

What is test-retest reliability?

Assessing the same measure on the same people at different times and computing the correlation coefficient.

What is parallel forms reliability?

Assessing the consistency of results from two tests constructed from the same content domain.

What is inter-rater reliability?

The degree to which different raters give consistent estimates of the same phenomenon.

What is internal consistency reliability?

The consistency of results across items within a test.

What is Cronbach's Alpha?

A measure of internal consistency that looks at the pattern of correlations among all items.

What is the relationship between reliability and validity?

An unreliable measure always has low validity, but high reliability does not guarantee high validity.

What is internal validity?

The approximate truth about inferences regarding cause-effect relationships.

What are the three criteria for establishing a causal relationship?

Temporal precedence, covariation of the cause and effect, and no plausible alternative explanations.

What does temporal precedence refer to?

Showing that the cause happened before the effect.

What is covariation of the cause and effect?

Demonstrating that when X is present, Y is also present, and vice versa.

What is the third-variable problem?

The issue of ruling out other variables that may be causing the outcome.

What is a history threat in research?

Events occurring outside the research situation that affect participants' responses.

What does maturation threat refer to?

Natural changes over time that can affect participants' responses.

What is a testing threat?

When taking a pretest affects how participants perform on a posttest.

What is instrumentation threat?

Changes in the measure used to assess the dependent variable over time.

What is statistical regression?

The phenomenon where extreme scores move closer to the mean on subsequent measurements.

What is regression toward the mean?

The tendency for extreme scores to become less extreme on retesting.

What is a multiple group design in research?

A design involving at least two groups with before and after measurements.

What is the role of a control group in research?

To serve as a comparison group that does not receive the treatment or program.

What is the purpose of a control group in research?

To provide a comparison against the experimental group that does not receive the treatment.

What is selection bias?

A threat to internal validity that occurs when research participants in the control condition differ in some way from those in the experimental condition.

What are the three forms of selection bias?

Nonrandom assignment, use of preexisting groups, and mortality.

What is nonrandom assignment?

Assigning participants to conditions in a way that does not ensure equal representation, such as only including men in one group and women in another.

How can preexisting groups lead to selection bias?

When researchers must assign natural groups rather than individuals, leading to non-random assignment.

What does mortality refer to in research?

The dropout of participants from a study, which can skew results if certain characteristics are overrepresented among those who drop out.

What are social interaction threats?

Factors that affect research results due to social pressures in the research context.

What is diffusion or imitation of treatment?

When participants in the comparison group learn about the program from the program group, affecting their outcomes.

What is compensatory rivalry?

When the comparison group develops a competitive attitude towards the program group, potentially skewing results.

What is resentful demoralization?

When the comparison group feels discouraged or angry upon learning about the program group's treatment.

What is compensatory equalization of treatment?

When the control group receives a treatment designed to compensate for the program group's treatment.

How can researchers enhance internal validity?

By ensuring all participants have the same experience except for differences related to the independent variable.

What is external validity?

The degree to which study findings can be generalized to other settings, populations, or times.

What is generalizing across?

Determining if study results pertain to more than one setting, population, or subpopulation.

What is generalizing to?

Determining if study results pertain to a specific setting or population.

What is the sampling model approach?

A method where researchers draw a fair sample from a population to generalize results.

What is the proximal similarity model approach?

A method that considers the similarity of contexts to determine generalizability of study results.

What are threats to external validity?

Factors that may lead to incorrect generalizations, including differences in persons, places, and times.

How can researchers improve external validity?

By using random selection, ensuring maximum participation, and conducting studies in diverse settings.

What is a treatment confound?

A situation where participants experience different conditions that are not controlled, affecting the outcome.

What is a measurement confound?

Using measures that lack discriminant validity, leading to inaccurate conclusions.