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.)
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.)
