Statistical Hypothesis Testing Task

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A Statistical Hypothesis Testing Task is a statistical inference task for testing two opposing statistical hypotheses about a statistical population using data from samples.



  • (Changing Works, 2017) ⇒ Retrieved on 2017-05-07 from Copyright: Changing Works 2002-2016
    • There are two types of test data and consequently different types of analysis. As the table below shows, parametric data has an underlying normal distribution which allows for more conclusions to be drawn as the shape can be mathematically described. Anything else is non-parametric.
Parametric Statistical Tests Non-Parametric Statistical Tests
Assumed distribution Normally Distributed Any
Assumed variance Homogeneous Any
Typical data Ratio or Interval Ordinal or Nominal
Data set relationships Independent Any
Usual central measure Mean Median
Benefits Can draw more conclusions Simplicity; Less affected by outliers


Parametric tests (means) Nonparametric tests (medians)
1-sample t test 1-sample Sign, 1-sample Wilcoxon
2-sample t test Mann-Whitney test
One-Way ANOVA Kruskal-Wallis, Mood’s median test
Factorial DOE with one factor and one blocking variable Friedman test


Independent Sample t Test Mann-Whitney test
Paired samples t test Wilcoxon signed Rank test
One way Analysis of Variance (ANOVA) Kruskal Wallis Test
One way repeated measures Analysis of Variance Friedman's ANOVA



A hypothesis test examines two opposing hypotheses about a population: the null hypothesis and the alternative hypothesis. The null hypothesis is the statement being tested. Usually the null hypothesis is a statement of "no effect" or "no difference". The alternative hypothesis is the statement you want to be able to conclude is true.
Based on the sample data, the test determines whether to reject the null hypothesis. You use a p-value, to make the determination. If the p-value is less than or equal to the level of significance, which is a cut-off point that you define, then you can reject the null hypothesis.
A common misconception is that statistical hypothesis tests are designed to select the more likely of two hypotheses. Instead, a test will remain with the null hypothesis until there is enough evidence (data) to support the alternative hypothesis.
Examples of questions you can answer with a hypothesis test include:
  • Does the mean height of undergraduate women differ from 66 inches?
  • Is the standard deviation of their height equal less than 5 inches?
  • Do male and female undergraduates differ in height?


Ordinal and numerical measures
1 group N ≥ 30 One-sample t-test
N < 30 Normally distributed One-sample t-test
Not normal Sign test
2 groups Independent N ≥ 30 t-test
N < 30 Normally distributed t-test
Not normal Mann–Whitney U or Wilcoxon rank-sum test
Paired N ≥ 30 paired t-test
N < 30 Normally distributed paired t-test
Not normal Wilcoxon signed-rank test
3 or more groups Independent Normally distributed 1 factor One way anova
≥ 2 factors two or other anova
Not normal Kruskal–Wallis one-way analysis of variance by ranks
Dependent Normally distributed Repeated measures anova
Not normal Friedman two-way analysis of variance by ranks
Nominal measures
1 group np and n(1-p) ≥ 5 Z-approximation
np or n(1-p) < 5 binomial
2 groups Independent np < 5 fisher exact test
np ≥ 5 chi-squared test
Paired McNemar or Kappa
3 or more groups Independent np < 5 collapse categories for chi-squared test
np ≥ 5 chi-squared test
Dependent Cochran´s Q