Chapter 5 + Chapter 6 Stats Quiz #3

What Is a Test Statistic?

A standardized value that tells us how far our sample result is from what we would expect if the null hypothesis (H₀) were true

What is Expected variability

How much the difference could vary just by chance

What is the purpose of One Sample t-Test

Compare the mean of one sample to a known or hypothesized population mean

When to use One Sample t-Test

• One group

• You know the population mean

• Data is continuous

• Normally distributed

What is the purpose of Independent Sample t-Test (2-Sample t-Test)

Compare the means of two independent samples

When to use Independent Sample t-Test (2-Sample t-Test)

• Two unrelated groups

• Data is continuous

• Normally distributed

What are the two types of Independent Sample t-Tests

1. Equal variances assumed (pooled t-test)

2. Unequal variances assumed (Welch’s t-test)

What is the purpose of a Paired Sample t-Test

Compares the means of two related groups to see if there is a

significant difference

When to use a Paired Sample t-Test

• One group measured twice (pre-test vs post-test)

• Matched pairs (twins)

• Data is continuous

• Normally distributed

What is the purpose of the Wilcoxon Text

Non-parametric statistical test used to compare medians or distributions

What does the Wilcoxon Test not require

Normally distributed data

What are the two types of Wilcoxon Tests

• Wilcoxon Signed-Rank Test

• Wilcoxon Rank-Sum Test (Mann-Whitney U Test)

What are the advantages of Wilcoxon Tests

• Robust to outliers and non-normal data

• Suitable for ordinal, interval, or continuous data

When to use Wilcoxon Test

• Data is not normally distributed

• Small sample sizes

• Comparing medians rather than means

Purpose of Wilcoxon Signed-Rank Test

Compare paired data or a single sample median to a known

value

Purpose of Wilcoxon Rank-Sum Test (Man-Whitney U)

Compare medians of two independent samples

When to use Wilcoxon Signed-Rank Test

• Data is paired or comes from a single sample

• Differences between pairs are ordinal, interval or continuous

• Random sampling

When to use Wilcoxon Rank-Sum Test – Man-Whitney U

• Data is ordinal, interval, or continuous

• Two Samples are independent

• Random sampling

What test to use for normally distributed data and when comparing means

T-tests

What test to use for non-normal data or when comparing medians

Wilcoxon tests

When to use t-Tests

Data normally distributed

Comparing Means

When to use Wilcoxon Tests

Data non-normally distributed

Comparing Medians

What is the purpose of the Chi-Squared Test (X²) for Independence

To determine if two categorical variables are independent

When to use Chi-Squared Test (X2) for Independence

• Data is categorical

• Observations are independent

• Expected frequency in each cell is at least 5

What is the purpose of Proportion Tests

To test if the proportion of a categorical variable matches a hypothesized value or compares two proportions

When to use Proportion Tests

• Data is categorical

• Observations are independent

• Sample size is large enough (n ≥ 30)

Purpose of One Way ANOVA

Tests the difference between the mean scores of 3+ groups

When to use One Way ANOVA

• PARAMETRIC

• Normal distributed

• Kolmogorov-Smirnov, Shapiro-Wilk, or Q-Q plot

• Homogeneity of variance (equal variances in independent

groups)

• Sphericity

What is the Independent variable

The variable that we change/manipulate

What is the Dependent Variable

The variable that we measure

What is Systematic variance

Amount of variation in Dependent Variable that can be explained by the Independent Variable

What is Unsystematic Variance

Amount of variation in Dependent Variable that cannot be explained by the Independent Variable

How does ANOVA work

1. Calculate group means

2. Look at the deviation of each point from the group mean (random/unsystematic variance)

3. Calculate grand mean

4. Look at the differences between each group mean and grand mean (systematic variance)

Hypothesis Testing for ANOVA

ANOVA compares the amount of variation that can be explained by the IV to the amount left unexplained.

What does a large F value indicate`

Low p value

What does a low F value indicate

High p value

Total number of degrees of freedom:

total number of participants - 1

Systematic variance degrees of freedom:

total number of groups - 1

Unsystematic variance degrees of freedom:

total number of participants - total number of groups

What is Sphericity

The variance of the differences between the groups are homogenous

When do we reject Ho

P-value < 0.05 (significant difference)

When do we fail to reject Ho

P-value > 0.05 (no significant difference