statistics II

Population

Entire group of interest.

Sample

Subset of the population used for analysis.

Null hypothesis (H0)

Assumes no effect or no difference.

Alternative hypothesis (H1)

Assumes an effect or difference exists.

P‑value

Probability of observing data if the null hypothesis is true.

Significance threshold (α)

Cut‑off for rejecting H0 (commonly 0.05).

t‑test

Statistical test comparing means of two groups.

Independent t‑test

Compares means of two unrelated samples.

Paired t‑test

Compares means of paired or matched samples.

Test statistic (t)

Quantifies difference between means relative to variance.

Large t value

Indicates big difference or small variance.

Chi‑squared test

Compares observed vs expected frequencies.

Expected frequency

Value predicted if H0 is true.

Chi‑squared statistic (χ²)

Measures discrepancy between observed and expected values.

Rejecting H0

Occurs when p < α.