Statistical Tests
Test
Statistical Test Variables/Groups Purpose Degrees of Freedom Interpretation of Significance Example Data / Research Question
Stat.
Is the distribution of x O E “Are the observed sales
df = k – 1 The observed distribution of x
different from a Painting a b of art styles different
Goodness-of-Fit - 1 nominal variable (x) is significantly different from x Sculpture c d
known/theoretical from what would be
Chi- [k: no. categories] the expected distribution Sketch e f
distribution (p)? expected?”
Squared 𝛘2
x “Is pet type
Tests df = (r – 1) × (c – 1)
Independence/ - 1 nominal predictor (x) Are x and y associated or There is a significant Dog Cat
associated with treat
Association - 1 nominal outcome (y) independent? association between x and y Chicken a b
[r: rows, c: columns] y
Beef c d preference?
The mean of y significantly
Is the sample mean (y)
differs from “Is the average delivery time of
One-Sample - 1 continuous outcome (y) different from a known df = n – 1
known/theoretical value of μ Cuddly’s art different from the
value (μ)?
standard 5 days?”
The mean of y significantly
Is the mean (y) different
Independent- - 2 categorical groups (x) differs between the 2 groups Do cats like being petted more
between 2 independent df = n1 + n2 - 2
t-Tests Samples - 1 continuous outcome (y) t of x than birds?
groups?
There is a significant
- 2 related conditions (i.e., Is the mean difference df = n – 1 difference in y between the 2 Does a class of psychology
Paired-Samples T1 vs. T2) (y) between 2 related related conditions students have a higher average
- 1 continuous outcome (y) conditions ≠ 0? [n: no. pairs] on their exam or on their
assignment?
Do group means (y)
- 1 categorical predictor (2+
differ across categories At least 1 group mean of y is
1-Way groups; x) between = k – 1
of x (assuming significantly different
- 1 outcome (y) within = N – k Is the rainfall in
homogeneity of variance)?
total df = N – 1 Melbourne different
At least 1 group mean of y is across different months
Do group means (y)
- 1 categorical predictor (2+ significantly different (w/o of winter?
differ across categories [k: no. groups, N: total
Welch 1-Way groups; x) assuming equal variances). Uses
of x (w/o assuming no. observations]
ANOVAs - 1 outcome (y) F adjusted df to test for mean
homogeneity of variance)?
differences
factor a = a – 1 Does location and
- 2 categorical predictors What are the main & factor b = b – 1 One or both predictors (x) weekday/end have effects
2-Way (2+ groups) interaction effects of interaction = (a -1)×(b-1) significantly affect y (and/or (individual or joint) on
- 1 outcome (y) each x on y? error = N – a×b there’s an interaction) lemonade sales?
total df = N – 1
regression model = 1 Do changes in UV level
- 1 continuous predictor (x) Does change in x predict Changes in x significantly
Linear residual = n – 2 predict changes in the
- 1 continuous outcome (y) change in y? predict changes in y
total df = n – 1 no. sunscreen sold?
Regressions F&t regression model = p
Do changes in multiple residual = n – p – 1 One or more predictors (x) Do changes in UV
- 2+ predictors (x) level and temperature
Multiple x’s predict change in y? total df = n – 1 significantly predict y (after
- 1 continuous outcome (y) predict changes in the
( joint & unique effects) controlling for the others)
[p: no. predictors] no. sunscreen sold?
Non-Parametric Tests
Test Variables Purpose/Use Statistical Test Test Stat. Interpretation of Significance
There is a significant difference in proportions between the
McNemar’s - 2 related categorical variables When assumption of independence is violated 𝛘2
paired groups
𝛘2 test
When assumption of ‘large’ (> 5) expected
Fischer Exact - 2 categorical variables p-value There is a significant association between the 2 variables
frequencies is violated, used w. 2x2 crosstab tables
Wilcoxon - 2 related continuous variables When data is not normally distributed t-test W The median difference between paired scores ≠ 0
- 1 categorical (3+ groups) When assumption of normally distributed residuals One or more groups differ significantly in their medians (not
Kruskal-Wallis 1-Way ANOVA H
- 1 continuous variable is violated mean)
Test
Statistical Test Variables/Groups Purpose Degrees of Freedom Interpretation of Significance Example Data / Research Question
Stat.
Is the distribution of x O E “Are the observed sales
df = k – 1 The observed distribution of x
different from a Painting a b of art styles different
Goodness-of-Fit - 1 nominal variable (x) is significantly different from x Sculpture c d
known/theoretical from what would be
Chi- [k: no. categories] the expected distribution Sketch e f
distribution (p)? expected?”
Squared 𝛘2
x “Is pet type
Tests df = (r – 1) × (c – 1)
Independence/ - 1 nominal predictor (x) Are x and y associated or There is a significant Dog Cat
associated with treat
Association - 1 nominal outcome (y) independent? association between x and y Chicken a b
[r: rows, c: columns] y
Beef c d preference?
The mean of y significantly
Is the sample mean (y)
differs from “Is the average delivery time of
One-Sample - 1 continuous outcome (y) different from a known df = n – 1
known/theoretical value of μ Cuddly’s art different from the
value (μ)?
standard 5 days?”
The mean of y significantly
Is the mean (y) different
Independent- - 2 categorical groups (x) differs between the 2 groups Do cats like being petted more
between 2 independent df = n1 + n2 - 2
t-Tests Samples - 1 continuous outcome (y) t of x than birds?
groups?
There is a significant
- 2 related conditions (i.e., Is the mean difference df = n – 1 difference in y between the 2 Does a class of psychology
Paired-Samples T1 vs. T2) (y) between 2 related related conditions students have a higher average
- 1 continuous outcome (y) conditions ≠ 0? [n: no. pairs] on their exam or on their
assignment?
Do group means (y)
- 1 categorical predictor (2+
differ across categories At least 1 group mean of y is
1-Way groups; x) between = k – 1
of x (assuming significantly different
- 1 outcome (y) within = N – k Is the rainfall in
homogeneity of variance)?
total df = N – 1 Melbourne different
At least 1 group mean of y is across different months
Do group means (y)
- 1 categorical predictor (2+ significantly different (w/o of winter?
differ across categories [k: no. groups, N: total
Welch 1-Way groups; x) assuming equal variances). Uses
of x (w/o assuming no. observations]
ANOVAs - 1 outcome (y) F adjusted df to test for mean
homogeneity of variance)?
differences
factor a = a – 1 Does location and
- 2 categorical predictors What are the main & factor b = b – 1 One or both predictors (x) weekday/end have effects
2-Way (2+ groups) interaction effects of interaction = (a -1)×(b-1) significantly affect y (and/or (individual or joint) on
- 1 outcome (y) each x on y? error = N – a×b there’s an interaction) lemonade sales?
total df = N – 1
regression model = 1 Do changes in UV level
- 1 continuous predictor (x) Does change in x predict Changes in x significantly
Linear residual = n – 2 predict changes in the
- 1 continuous outcome (y) change in y? predict changes in y
total df = n – 1 no. sunscreen sold?
Regressions F&t regression model = p
Do changes in multiple residual = n – p – 1 One or more predictors (x) Do changes in UV
- 2+ predictors (x) level and temperature
Multiple x’s predict change in y? total df = n – 1 significantly predict y (after
- 1 continuous outcome (y) predict changes in the
( joint & unique effects) controlling for the others)
[p: no. predictors] no. sunscreen sold?
Non-Parametric Tests
Test Variables Purpose/Use Statistical Test Test Stat. Interpretation of Significance
There is a significant difference in proportions between the
McNemar’s - 2 related categorical variables When assumption of independence is violated 𝛘2
paired groups
𝛘2 test
When assumption of ‘large’ (> 5) expected
Fischer Exact - 2 categorical variables p-value There is a significant association between the 2 variables
frequencies is violated, used w. 2x2 crosstab tables
Wilcoxon - 2 related continuous variables When data is not normally distributed t-test W The median difference between paired scores ≠ 0
- 1 categorical (3+ groups) When assumption of normally distributed residuals One or more groups differ significantly in their medians (not
Kruskal-Wallis 1-Way ANOVA H
- 1 continuous variable is violated mean)
