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When and How to Use Each Hypothesis Test

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  • When to use a Z-test

    Use a Z-test when the population variance is known and the sample size is large (usually n > 30).

  • When to use a one-sample t-test

    Use a one-sample t-test to compare the sample mean to a known value when the population variance is unknown and the sample size is small.

  • When to use a two-sample t-test

    Use a two-sample t-test to compare the means of two independent groups when population variances are unknown.

  • When to use a paired t-test

    Use a paired t-test to compare means from the same group at different times or under different conditions.

  • When to use a one-tailed hypothesis test

    Use a one-tailed test when the research hypothesis predicts a direction of the effect.

  • When to use a two-tailed hypothesis test

    Use a two-tailed test when the research hypothesis does not predict the direction of the effect.

  • How to set up null and alternative hypotheses

    The null hypothesis (H0) states no effect or difference; the alternative hypothesis (H1) states the expected effect or difference.

  • How to choose significance level (alpha)

    Choose alpha (commonly 0.05) as the threshold probability to reject the null hypothesis.

  • How to interpret p-value

    If the p-value is less than alpha, reject the null hypothesis; otherwise, fail to reject it.

  • When to use a test for proportions

    Use a z-test for proportions to compare sample proportions to a population proportion or between two groups.

  • When to use a nonparametric test

    Use nonparametric tests when data do not meet normality assumptions or are ordinal.

  • When to use a correlation test

    Use a correlation test to assess the strength and direction of a linear relationship between two continuous variables.

  • When to use a regression hypothesis test

    Use a regression test to determine if predictor variables significantly explain variation in the response variable.

  • How to check assumptions before hypothesis testing

    Check assumptions like normality, independence, and equal variances before choosing and performing a hypothesis test.

  • How to use degrees of freedom in t-tests

    Degrees of freedom depend on sample size and affect the critical values in t-distribution tables.

  • How to decide between independent and paired tests

    Use independent tests for separate groups and paired tests for related or matched samples.