Statistical Concepts: Sample Means, Hypothesis Testing, and Correlation

What is the distribution of sample means?

The collection of sample means for all possible random samples of a particular size that can be obtained from a population.

What does the Central Limit Theorem state?

It applies to any population with a mean and standard deviation, stating that the mean of the distribution of sample means equals the population mean.

How does sample size affect the distribution of sample means?

The larger the sample size, the closer the sample means will be to the population mean, as per the law of large numbers.

What is the formula for the standard error of the mean (σM)?

The standard error of the mean can be found by dividing the standard deviation (σ) by the square root of the sample size (√n).

What is a null hypothesis (H0)?

It states that there will be no relationship between the variables or that the relationship is in the opposite direction of the stated hypothesis.

What is an alternate hypothesis (H1)?

It states that a relationship exists between the variables in the direction stated.

What are critical regions in hypothesis testing?

Extreme scores that are unlikely to be observed if the hypothesis is false, denoted as an alpha level (α).

What does an alpha level (α) represent in hypothesis testing?

It represents the percentage chance that the observed results were obtained due to random chance, indicating a real relationship.

What is a Type 1 error?

A false-positive where the null hypothesis is rejected even though no true relationship exists.

What is a Type 2 error?

A false-negative where the null hypothesis is not rejected even though a true relationship exists.

What does correlation measure?

It describes the relationship between two variables, denoted as an r-value, ranging from -1 to 1.

What do positive correlations indicate?

When the value of one variable increases, the value of the other variable also increases.

What do negative correlations indicate?

When the value of one variable increases, the value of the other variable decreases.

What is the limitation of correlation?

Correlations can only show relationships between variables; they do not establish causation.

How do outliers affect correlation values?

Correlations are sensitive to outliers, which can pull correlation values toward them.

What is range restriction in correlation analysis?

Excluding portions of a population from analysis will weaken the observed relationship between variables.

What are linear relationships?

Relationships that are consistent regardless of the intensity of the variables, accurately represented by a straight line.

What are curvilinear relationships?

Relationships that change based on the relative intensity of the variables, such as stress and productivity.

What is Pearson correlation?

The most commonly used correlation, best for linear relationships, requiring interval or ratio-scale data.

What is Spearman correlation?

Used when data are ordinal or to measure the consistency of a curvilinear relationship.

What is the coefficient of determination (r2)?

It gives the proportion of variance in one variable accounted for by changes in another variable.

What is the difference between direct questioning and third-party reports?

Direct questioning is good for measuring unobservable things, while third-party reports help identify bias in self-reports.

What are the four types of measurement scales?

Nominal, ordinal, interval, and ratio.

What is reliability in measurement?

The consistency of measurement, represented by a correlation coefficient.

What is validity in measurement?

The accuracy of inferences made from the results of a test or measure.

What are the three types of validity?

Content validity, construct validity, and criterion validity.

What is the difference between trinitarian and unitarian validity?

Trinitarian validity views content, construct, and criterion validity as distinct, while unitarian validity sees them as contributing to an overall concept of validity.