Overview of all statistical tests of both the courses Statistics 1 & Statistics 2.
E.g. including the tests: Chi2, ANOVA, linear regression and non-parametric alternatives. Each test is accompanied by the associated cases, variables, objectives and requirements, which you can base the three key qu...
Statistical Tests 2.0
Cases Variables Objective Requirements
Single sample Independent Ratio variable (or Establish whether the population Normal distribution or sufficient
t-test cases interval) mean corresponds with a test amount of cases
value
Paired Independent One ratio variable Determine whether there is a Paired observations + Differences
samples t-test pairs (or interval) difference between two normally distributed or sufficient
population means when the amount of cases
observations are paired
Non Wilcoxon Independent One ratio variable Differences between 2 paired Paired observations + Differences
parametric signed-rank pairs (or interval) groups. Objective same as paired have a symmetric distribution
alternative test samples t-test, back-up plan if it
doesn’t meet requirements. Also
gives the size of the difference.
Non Sign test Independent One ordinal or For each pair: determine sign of Paired observations
parametric pairs ratio variable (or difference. (Not size of
alternative interval) difference.)
Two samples Independent Ratio variable (or Determine whether the means Two groups + Each group: normal
t-test cases interval) for two populations are equal distribution or sufficient amount of
cases
Non Mann- Independent Ordinal or ratio Determine whether the medians Two groups (+ Group distributions
parametric Whitney test cases variable (or for two populations are equal. have similar shapes; doesn’t have
alternative interval) to be mentioned explicitly)
Centrality!
Non Two samples Independent Ordinal or ratio Determine whether the Two groups. One-sided.
parametric number-of- cases variable (or distributions (explicitly
alternative runs test interval) mentioned) for a variable X are
similar between two groups
Kolmogorov- Independent Ordinal and Normality check Works less good when the data is
Smirnov and cases nominal not small (but that’s everywhere).
Shapiro-Wilk possible, ratio or Normality!
test interval
Levene’s test Independent Ratio variable (or Determine whether the variances Significant? We reject H0 + We
cases interval), two for two populations are equal assume variances are not equal
groups
Single sample Independent Ratio or interval Establish whether the population Normal distribution or sufficient
z-test cases scale, σ known mean corresponds with a test amount of cases + Population
value Standard Deviation known
(otherwise t-test)
Example of Binomial test Independent Binary variable Determine whether the Need binary variable and a test
non- cases proportion in a population proportion
parametric matches a test proportion.
test Describes proportion of
“successes” (and failures).
Example of Difference of Independent Binary variable Determine whether there is a Two groups (= 1 extra requirement
non- proportions cases difference in proportions compared to the binomial test)
parametric test between two groups. (Similar to
test two-sample t-test.)
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