HYPOTHESIS TESTING

Hypothesis testing is a statistical method used to make decisions or inferences about population parameters based on sample data.

Understand the significance of Type I and Type II errors in statistical tests and how they impact decision-making.

Follow these steps to perform a hypothesis test effectively: defining hypotheses, selecting a significance level, conducting the test, and interpreting results.

Learn what the P-value represents, its role in hypothesis testing, and how to use it effectively.

The power of a test measures the ability of a statistical test to detect an effect when there is one

The Bonferroni correction controls the risk of false positives when running many hypothesis tests at once, by dividing the significance threshold by the number of tests.

Learn how to perform hypothesis testing for a population mean, whether you know the population variance or not, and the scenarios where it applies.

Learn how to perform hypothesis tests for variance, which are essential for comparing the variability of different populations or ensuring process consistency.

Learn how to perform hypothesis testing for proportions, a fundamental technique in statistics used to compare population proportions with a specific value or with each other.

The one-sample z-test tests whether a population mean equals a specific value when the population standard deviation is known.

The F-test evaluates whether two populations have equal variances, using the ratio of their sample variances and the F distribution.

Welch's t-test compares the means of two independent groups without assuming equal population variances, making it more robust than the pooled t-test.

The two-sample z-test compares two population proportions using a pooled estimate under the null hypothesis of equal proportions.

The paired t-test compares two related measurements on the same subjects by reducing the problem to a one-sample test on the differences.

Learn about Analysis of Variance (ANOVA), a fundamental statistical technique used to determine whether there are significant differences between the means of three or more groups.

Tukey's HSD test compares every pair of group means after a significant ANOVA, controlling the familywise error rate so the overall false positive risk stays at the chosen alpha.

Bartlett's test checks homogeneity of variance across two or more groups, assuming the data are normally distributed. It is more powerful than Levene's test when that assumption holds, and less reliable when it doesn't.

Learn how to perform and interpret the Chi-square test, a key statistical tool for examining the association between categorical variables.

Learn how to apply the Kolmogorov-Smirnov (Lilliefors) test, a nonparametric test used to evaluate the goodness of fit for a sample distribution against a reference distribution.

The Shapiro-Wilk test is a powerful tool for assessing whether a given sample comes from a normally distributed population. It is particularly useful in small sample sizes.

Learn about the Jarque-Bera test, a statistical test that checks the normality of a dataset by examining its skewness and kurtosis.

Learn how to perform and interpret the Sign test, a nonparametric alternative to the paired t-test that makes no assumptions about the distribution of the data.

Learn how to apply and interpret the Wilcoxon test, a versatile nonparametric method used for hypothesis testing on paired or independent samples without assuming normality.

Understand the Ljung-Box test, a crucial tool for identifying autocorrelation in time series data, and learn how to apply it effectively.

The Kruskal-Wallis test is the nonparametric alternative to one-way ANOVA, comparing three or more independent groups using ranks instead of raw values.

Fisher's exact test computes an exact p-value for small contingency tables, using the hypergeometric distribution instead of the chi-square approximation.

Levene's test checks whether two or more groups have equal variances, without assuming the data are normally distributed.

McNemar's test compares paired binary outcomes measured on the same subjects, such as before/after or two raters on the same cases, using only the pairs that disagree.