Understanding Null Hypothesis Significance Testing (NHST)

Null Hypothesis

Assumes no difference in population means.

Alternative Hypothesis

Claims a difference exists between population means.

Alpha Level

Threshold for rejecting the null hypothesis, often 0.05.

Test Statistic

Value calculated to determine significance of results.

Causal Hypothesis

Predicts one variable influences another.

Association Hypothesis

Suggests a relationship exists between variables.

Type 1 Error

Rejecting null hypothesis when it is true.

Type 2 Error

Failing to reject null hypothesis when it is false.

Critical Region

Values leading to rejection of the null hypothesis.

Critical Value

Boundary defining critical region in hypothesis testing.

Z Test

Statistical test for comparing sample and population means.

Population Mean

Average score of the entire population, e.g., 50.

Standard Deviation

Measure of variability in a set of scores, e.g., 10.

P Value

Probability of obtaining results if null hypothesis is true.

Dichotomous Thinking

Decision-making between two exclusive alternatives.

Estimation Thinking

Focuses on the magnitude of effects or differences.

Meta-analytic Thinking

Contextualizes results within broader research findings.

Nondirectional Test

Tests for any difference without a specific direction.

Directional Test

Tests for a specific increase or decrease in means.

Research Hypothesis

Testable claim about psychological constructs.

Sampling Distribution

Distribution of sample statistics under the null hypothesis.

Statistical Power Analysis

Determines likelihood of detecting an effect if it exists.

Math Achievement Test (MAT)

Assessment used to measure students' math skills.

Population Parameters

Characteristics of the population, such as mean and SD.

NHST

Null Hypothesis Significance Testing; evaluates evidence against H0.

P-value

Probability of observing data if H0 is true.

Frequentist Approach

Focuses on long-run frequency of events.

Bayesian Approach

Updates probability of H0 based on data.

Effect Size

Quantitative measure of the magnitude of a phenomenon.

Cohen's d

Standardized difference between two means.

Standard Error

Estimate of the variability of a sample statistic.

Confidence Interval (CI)

Range estimating population parameter with specified confidence.

Parametric Tests

Assumes underlying population distribution (e.g., t-tests).

Nonparametric Tests

Does not assume a specific population distribution.

Chi-Square Test

Tests relationships between categorical variables.

Goodness of Fit Test

Assesses if observed frequencies match expected frequencies.

Test of Independence

Examines association between two categorical variables.

Degrees of Freedom (df)

Number of values free to vary in calculations.

Observed Frequencies

Actual counts collected from a sample.

Expected Frequencies

Counts predicted under the null hypothesis.

Adjusted Standardized Residuals

Indicates how far observed frequencies deviate from expected.

Odds Ratio (OR)

Ratio of odds of an event occurring in two groups.

Statistically Significant

Results unlikely due to chance, typically p < 0.05.

Chi-Square Statistic

Test statistic used in chi-square tests.

Sample Size (n)

Number of observations in a study.

Null Hypothesis (H0)

Assumes no effect or difference exists.

Alternative Hypothesis (H1)

Assumes a significant effect or difference exists.

Joint Probabilities

Probability of two events occurring together.

Conditional Probabilities

Probability of an event given another event.

Chi-Square Test Assumptions

Expected frequencies > 5; data independence.

Phi Coefficient

Effect size measure for 2x2 contingency tables.

Cramer's V

Effect size measure for larger contingency tables.

Anastasia

Tutor with 15 students in study.

Bernadette

Tutor with 18 students in study.

Dependent Variable (DV)

Final grade in the course being measured.

Research Question

Which tutor is more effective in teaching?

Interval Scale

Scale where differences between values are meaningful.

Normality

Assumption that data follows a normal distribution.

Skewness

Measure of asymmetry in a distribution.

Kurtosis

Measure of tailedness in a distribution.

Shapiro-Wilks Test

Tests if data significantly differs from normal distribution.

Homogeneity of Variance

Assumption that variances are equal across groups.

Levene's Test

Tests for equal variances between groups.

Brown-Forsythe Test

Tests for equal variances when sample sizes differ.

Independent t-test

Compares means of two independent groups.

Cohen's d

Standardized effect size measure for comparing means.

Glass' Delta

Effect size using one group's standard deviation.

Confidence Interval

Range estimating the true difference between means.

Mann-Whitney U Test

Nonparametric test for comparing two independent groups.

Probability of Superiority (PS)

Chance one score is greater than another.

Rank-Biserial Correlation

Correlation between nominal and ordinal variables.

Statistical Power

Probability of correctly rejecting a false null hypothesis.

Two-Sided Test

Tests for effects in both directions.

Sample Size

Number of participants included in a study.

Effect Size in Population

Magnitude of effect size influencing power.