Module 4

Hypothesis Testing

A statistical method used to make decisions or inferences about population parameters based on sample data.

Null Hypothesis (H0)

A statement that indicates there is no effect or no difference, and is the hypothesis that researchers aim to reject.

Alternative Hypothesis (H1)

A statement that indicates there is an effect or a difference, and it opposes the null hypothesis.

P-value

The probability of observing a test statistic at least as extreme as the one observed, under the assumption that the null hypothesis is true.

Significance Level (Alpha)

The threshold for determining whether to reject the null hypothesis, commonly set at 0.05.

One Sample T-Test

A statistical test used to compare the mean of a single sample to a known value or population mean.

Two Tailed Hypothesis

A hypothesis that tests for the possibility of an effect in two directions, above and below the specified value.

T-Statistic

A ratio that compares the mean difference to the standard deviation, indicating how far the sample mean is from the population mean.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Confidence Interval

A range of values derived from sample statistics that is likely to contain the true population parameter.

Effect Size

A quantitative measure of the magnitude of a phenomenon; indicates the strength of a relationship.

Cohen's d

A measure of effect size that indicates the standardized difference between two means.

ANOVA (Analysis of Variance)

A statistical procedure used to compare means across multiple groups and assess if at least one group mean is different from others.

Post Hoc Analysis

Follow-up tests conducted after ANOVA to determine which specific group means are significantly different.

Independent Sample T-Test

A statistical test used to compare the means of two unrelated groups.

Paired Sample T-Test

A statistical test used to compare means from the same group at different times.

Variance

A statistical measurement of the spread between numbers in a data set.

Non-Directional Hypothesis

A hypothesis that does not predict the direction of the effect or relationship.

Directional Hypothesis

A hypothesis that predicts the direction of the expected difference or relationship.

Sampling Error

The difference between the sample statistic and the actual population parameter.

Type I Error

The error made when the null hypothesis is rejected when it is actually true.

Type II Error

The error made when the null hypothesis is not rejected when it is false.

Levene's Test

A statistical test used to assess the equality of variances for a variable calculated for two or more groups.

Significance Test

A statistical procedure that determines if the observed data deviates significantly from what would be expected under the null hypothesis.

Standard Error

An estimate of the variability of the sample mean from the population mean.

Two-Way ANOVA

An extension of ANOVA that involves two independent variables.

Random Assignment

The process of randomly assigning subjects to different treatment groups to ensure each subject has an equal chance of being assigned to any group.

Research Question

A specific query the researcher aims to answer through their study.

Descriptive Statistics

Statistics that summarize the data collected in a study, providing simple summaries about the sample and measurements.

Inferential Statistics

A set of statistical techniques that allows conclusions to extend beyond the immediate data alone.

Sample Size

The number of subjects or observations included in a study or sample.

Mean Difference

The difference between the average values of two groups.

Normal Distribution

A continuous probability distribution characterized by a bell-shaped curve, where most observations cluster around the central peak.

Confidence Level

The percentage that reflects how sure one can be about their confidence interval contains the true population parameter.

Research Hypothesis

The hypothesis that has a specific outcome predicted based on theory or previous research.

Statistical Significance

A determination that a result is unlikely to have occurred by chance alone, typically indicated by a p-value less than a predetermined threshold.

Causal Relationship

A relationship between two variables where one causes a change in the other.

Data Analysis

The process of inspecting, cleaning, and modeling data with the goal of discovering useful information.

Generalizable Results

Findings from a study that can be applied to or found in a broader population.

Chi-Square Test

A non-parametric test used to determine whether there is a significant association between two categorical variables.

Reliability

The degree to which a measure is consistent and stable over time.

Validity

The extent to which a test measures what it claims to measure.

H0: μ1 = μ2

The null hypothesis indicating that the means of two groups are equal.

H1: μ1 ≠ μ2

The alternative hypothesis indicating that the means of two groups are not equal.

Outliers

Data points that differ significantly from other observations, potentially skewing results.

Correlation Coefficient

A numerical measure of the strength and direction of a relationship between two variables.

Regression Analysis

A statistical method for estimating the relationships among variables, often used for prediction.

Chi-Square Goodness of Fit Test

A statistical test to determine whether a sample data matches a population with a specified distribution.