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By Professor Omar Hasan Kasule Sr.

Learning Objectives:

Parametric Inference on 2 means  using the t statistic

Parametric Inference on 3 or more sample means using the F test (ANOVA).

Definition, properties, and uses of the non-parametric methods

Strengths and weaknesses of non-parametric methods

Parametric and non-parametric methods: correspondence and comparison


Key Words and Terms:

Analysis of variance, ANOVA

Non-parametric test statistic, Friedman

Non-parametric test statistic, Kendall-Wallis

Non-parametric test statistic, rank sum test

Non-parametric test statistic, signed rank test

Non-parametric test, sign test

Parametric test statistic,  t statistic (Student t test)

Parametric test statistics, F statistic

Parametric test statistics, z statistic




Inference on numeric continuous data is based on the comparison of sample means. Three test statistics are commonly used: z, t- and F-statistics. The z-statistic is used for large samples. The t and F are used for small or moderate samples. The z-statistic and the t-statistic are used to compare 2 samples. The F statistic is used to compare 3 or more samples.


The student t-test is the most commonly used test statistic for inference on continuous numerical data. It is defined for independent and paired samples. It is robust and can give valid results even if the assumptions of normal distribution and equal variance are not perfectly fulfilled. It is used uniformly for sample sizes below 60 and for larger samples if the population standard deviation is not known. For larger samples there is no distinction between testing based on the z statistic and testing based on the t statistic.


The F-test is a generalized test used in inference on 3 or more sample means in procedures called analysis of variance, ANOVA.



Non-parametric methods are about 95% as efficient as the more complicated and involved parametric methods. They are simple, easy to understand, and easy to use. They work well for small data sets but not for large data sets. Virtually each parametric test has an equivalent non-parametric one.  Specialized computer programs can carry out all the non-parametric tests: the sign test, the signed rank test, the rank sum test, the Kruskall-Wallis test, and the Friedman test.

Professor Omar Hasan Kasule August 2005