Comprehensive Quizlet: Key Concepts in Hypothesis Testing, ANOVA, and t-Tests for Psychology and Statistics

What does an alpha level represent?

A probability cutoff that defines which scores are considered unlikely to occur if the null hypothesis is true (0.05 standard alpha level)

Define p-value.

Probability of obtaining a sample statistic as/or more extreme than the observed if null hypothesis is true

What is statistical power?

The probability that a test will correctly reject the null hypothesis when the treatment actually has a real effect.

What is a Type I error?

A false positive: rejecting a true null hypothesis and falsely concluding a treatment has an effect.

What is a Type II error?

A false negative: failing to reject a false null hypothesis and falsely concluding a treatment has no effect.

What is the probability of a Type I error equal to?

The alpha level.

When are you more likely to make a Type II error?

When the treatment effect is small or the sample size is small.

What is the purpose of a z-test?

Use single sample mean from a known population (known mean and sd) to test hypotheses about an unknown population

What is the relationship between the critical value and the critical region?

The critical value defines the boundary of the critical region; sample statistics beyond this value fall into the critical region.

How does the t-statistic formula differ from the z-score formula?

The t-statistic uses an estimated standard error based on sample statistics, whereas the z-score uses the true standard error based on population parameters.

What is a one-sample t-test?

Used to compare the mean of a single sample with a known population mean but unknown sd

What is an independent samples t-test?

Used to compare the mean of one group with the mean of a different, independent group.

What is a paired samples t-test?

Used to compare the means of two groups that are matched or connected

What is the purpose of the t-distribution?

It represents the sampling distribution of sample means converted to t-statistics, used when the population standard deviation is unknown.

Define degrees of freedom in the context of a t-test.

The number of scores in a sample that are statistically independent and free to vary after the sample mean has been calculated.

What is the core logic behind the One-way ANOVA?

Comparing systematic between-group variance to random within-group variance.

What does within-treatment variance measure?

The differences that exist inside each group, which serves as a measure of sampling error.

What does between-treatment variance measure?

The differences between group means, which reflects both the treatment effect and random sampling error.

How is the F-statistic calculated in an ANOVA?

(between-treatment variance) / (within-treatment variance)

What does an F-ratio near 1.00 indicate?

It indicates that the null hypothesis is likely true, meaning there are no significant differences between treatment effects.

What does a large F-ratio indicate?

It indicates a large treatment effect, suggesting that the sample mean differences are greater than what would be expected by chance.

In the context of ANOVA, what is another term for variance?

Mean square.

Why is a one-way ANOVA referred to as an 'omnibus' test?

Because it tests the equality of all group means simultaneously rather than comparing them in pairs.

What is the primary limitation of the omnibus ANOVA test?

It indicates that at least one mean difference exists but does not specify which specific treatments are different from each other.

What is the main drawback of using Tukey's Honestly Significant Difference (HSD) test?

It only works with even sample sizes and is fairly liberal, meaning it does not control the Type I error rate as effectively as other tests.

What is a key benefit of the Scheffé test compared to Tukey's HSD?

It works with uneven group sizes and is more conservative, providing better control over the Type I error rate.

How is a factorial design represented?

It is represented as a matrix where the levels of Factor A are rows and the levels of Factor B are columns.

In a 2 x 2 factorial design, how many experimental groups are there?

Four experimental groups.

What is a 'main effect' in a factorial ANOVA?

The mean difference between the levels of a single factor, ignoring the other factor.

What is an 'interaction effect' in a factorial ANOVA?

It occurs when the effect of one factor on the dependent variable depends on the level of the other factor.

When should you be cautious about interpreting main effects?

When a significant interaction effect is present, as the main effects can be misleading.

How do you test the main effect of Factor A in a factorial design?

By testing the differences between the marginal means of Factor A, averaging over the levels of Factor B.

What is a disordinal interaction?

An interaction where the lines on an interaction plot cross each other.

What does it mean if the lines on an interaction plot are separated but parallel?

It suggests a main effect of the variable that defines the lines, but no interaction.

What does it mean if the lines on an interaction plot slope up or down?

It is consistent with a main effect of the variable on the horizontal axis.

What is the null hypothesis for an interaction effect in a two-factor ANOVA?

There is no interaction effect between Factor A and Factor B.

What is the structure of the F-ratio in terms of error?

F = (treatment effect + sampling error) / sampling error.

How does total degrees of freedom (df) affect the F-distribution?

The higher the total df, the more closely the possible F-ratios under the null hypothesis cluster around 1.0.

What does the Scheffé test require for significance?

The F-value calculated between two specific groups must exceed the critical F-value used for the omnibus test.

What is the difference between within-group variance and between-group variance in ANOVA?

Within-group variance represents random error, while between-group variance represents both error and the treatment effect.

What are the two main ways to interpret two-factor ANOVAs?

Using a matrix of cell means or a plot of the interaction.

Critical region

region of distribution that contains very unlikely outcomes if null hypothesis is true