Understanding t-Tests in Statistical Analysis

Dependent variable

Numerical variable influenced by independent variable.

Independent variable

Categorical variable that affects dependent variable.

Logistic regression

Used for binary outcome variables.

Linear regression

Analyzes relationships between numerical variables.

Contingency table analysis

Examines relationships between categorical variables.

One sample t-test

Compares sample mean to population mean.

t score formula

t = (x - μ) / s.

Standard error of the mean

Standard deviation of sampling distribution of mean.

t-distribution

Family of distributions with fatter tails.

Degrees of freedom

Calculated as n - 1 for one sample t-test.

Central Limit Theorem

Sampling distribution approaches normality with large n.

Hypothesis testing

Process of establishing null and alternative hypotheses.

Null hypothesis (H0)

Assumes no difference between sample and population.

Alternative hypothesis (H1)

Indicates a difference exists between sample and population.

p-value

Probability of observing data under null hypothesis.

Critical t table

Used to determine significance of t score.

Alpha level (α)

Threshold for rejecting null hypothesis, commonly 0.05.

Fail to reject null hypothesis

Insufficient evidence to support alternative hypothesis.

Sample mean (X)

Average score of the sample group.

Population mean (μ)

Expected average score of the population.

Standard deviation (SD)

Measure of variability within a sample.

Sample size (n)

Number of observations in the sample.

Dependent samples t-test

Compares scores of matched pairs.

One-sample t-test

Compares group mean to population norm.

Paired samples t-test

Another name for dependent samples t-test.

Difference scores

Scores calculated from paired observations.

Standard error

Measure of variability in sample means.

Degrees of freedom (df)

Calculated as n - 1 for paired samples.

Null hypothesis (H0)

Assumes no difference between group means.

Alternate hypothesis (H1)

Assumes a difference exists between group means.

t-statistic

Ratio of mean difference to standard error.

t-critical

Value from t-distribution for significance testing.

Significance level (α)

Probability of making a Type I error.

Homogeneity of variance

Assumption that variances of groups are equal.

Levene's F test

Tests for homogeneity of variances.

Pooled variance

Weighted average of variances from two samples.

Standard deviation (SD)

Measure of variability in a dataset.

t-calc

Calculated t-statistic from sample data.

t-table

Reference for critical t-values based on df.

Mean difference

Difference between group means in t-test.

Type I error

Rejecting H0 when it is true.

Type II error

Failing to reject H0 when it is false.

Normality assumption

Dependent variable should be normally distributed.

Sample size (n)

Number of pairs in dependent samples.

Before and after therapy

Common context for dependent samples t-test.

Statistical significance

Indicates if results are unlikely due to chance.

Degrees of Freedom (df)

Calculated as n - 1 for samples.

tcalc

Calculated t-value from sample data.

tcritical

Value obtained from critical t table.

Independent Samples T-Test

Compares means of two independent groups.

Mean Stress Level Before Treatment

M = 64.63, SD = 11.67.

Mean Stress Level After Treatment

M = 61.88, SD = 9.33.

t(7)

t-value with 7 degrees of freedom.

p > 0.05

Indicates no significant difference found.

Standard Error

Estimate of the variability of sample means.

Homogeneity of Variance

Variance of groups should be equal.

Levene's F Test

Tests for homogeneity of variance.

Pooled Variance

Weighted average of two sample variances.

t Statistic Formula

t = (x̄1 - x̄2) / SE.

Sample Size Impact

Larger sizes yield more reliable t values.

Alternative Hypothesis (H1)

Assumes a difference exists between means.

Two-Tailed Test

Tests for differences in both directions.

Level of Significance (α)

Threshold for rejecting the null hypothesis.

Standard Deviation Calculation

Measures variability within a sample.

Robustness of t-Test

Resilient to minor violations of assumptions.

Sample Design Types

Between-subjects and within-subjects designs.

tcritical

Critical t-value from statistical tables.

H0

Null hypothesis, no effect or difference.

M

Mean score of a sample.

SD

Standard deviation, measure of variability.

df

Degrees of freedom in statistical tests.

p-value

Probability of observing results under H0.

Cohen's d

Effect size measuring mean difference in SD units.

one-tailed test

Tests for differences in one direction.

α (alpha)

Significance level, probability of Type I error.

Effect size

Quantifies the magnitude of a difference.

Minimum r

Smallest correlation coefficient for effect size.

Minimum d

Smallest Cohen's d for effect size.

Psychological Bulletin

Journal where Kimmel's criteria were published.

Euzac

Antidepressant showing lower depression scores.

Prozac

Antidepressant with higher depression scores.

t(14)

t-value with 14 degrees of freedom.

Significance level

Threshold for determining statistical significance.