Hypothesis Testing and Statistical Significance Concepts

Population

Entire group from which samples are drawn.

Mean (Population)

Average value of a population, denoted as μ.

Standard Deviation (Population)

Measure of population data dispersion, denoted as σ.

Sample

Subset of the population used for analysis.

Mean (Sample)

Average value of a sample, denoted as M.

Standard Deviation (Sample)

Measure of sample data dispersion, denoted as SD.

Null Hypothesis

Assumes no difference or effect in research.

Research Hypothesis

Educated guess predicting study outcome.

Directional Hypothesis

Predicts a specific direction of effect.

Nondirectional Hypothesis

Predicts an effect without specifying direction.

Type I Error

Rejecting null hypothesis when it is true.

Type II Error

Failing to reject null hypothesis when it is false.

Significance Level

Probability threshold for rejecting null hypothesis.

Power

Ability to detect true effects in hypothesis testing.

Sampling Distribution

Distribution of sample means if null hypothesis is true.

Z Score

Standardized score indicating how many standard deviations away.

Normal Curve

Symmetrical bell-shaped distribution of data.

Skew

Asymmetry in distribution tails, indicating direction.

Kurtosis

Measure of the flatness of a distribution curve.

Significant Difference

Difference unlikely due to chance alone.

Obtained Value

Test statistic calculated during hypothesis testing.

Critical Value

Threshold for determining statistical significance.

Null Hypothesis Statement

Formal declaration of no effect or difference.

Research Question

Question guiding the formulation of hypotheses.

Evidence to Reject Null

Convincing data needed to disprove null hypothesis.

Observed Difference

Difference noted between sample groups in study.

Sample Variance

Variance of sample data, typically less than population variance.

Sample Size Impact

Larger samples reduce variance of sampling distribution.

Coin Flip Hypothesis

Testing if guesses exceed 50% accuracy.

Significance Level (α)

Threshold for rejecting the null hypothesis, typically 0.05.

Statistical Significance

Probability of data occurring if null hypothesis is true.

Effect Size

Magnitude of difference between sample and population means.

Confidence Interval

Range of values for the true population mean.

Power of a Test

Probability of correctly rejecting a false null hypothesis.

Z-Score

Standardized score indicating how many standard deviations away.

Standard Error (SE)

Standard deviation of the sampling distribution.

Two-Tail Test

Tests for deviations in both directions from the mean.

One-Tail Test

Tests for deviations in one direction from the mean.

Degrees of Freedom

Number of independent values in a statistical calculation.

Cohen's D

Effect size measuring distance in standard deviations.

Eta Squared (η²)

Proportion of variance attributed to group membership.

Region of Rejection

Area in distribution where null hypothesis is rejected.

Practical Significance

Real-world relevance of statistical findings.

Margin of Error

Range within which the true population parameter lies.

Z-Critical Value

Z-score threshold for significance in hypothesis testing.

Sample Size (N)

Number of observations in a sample.

Standard Deviation (SD)

Measure of data dispersion around the mean.

Normal Distribution

Symmetrical distribution where most values cluster around the mean.

P-Value

Probability of obtaining results as extreme as observed.

Hypothesis Testing

Method for making statistical inferences about populations.