With “Compare Numeric Values”, you can explore potential differences in numerical variables between groups.
From the analysis window, click "+ New analysis" and choose "Compare Numeric Values" from the dropdown menu.
Select the data model in the "Parameters" card on the right side. Select the series of interest from the dropdown menu if you choose to analyse series data.
Under "Compare", choose which of your numeric variables you want to compare
Then, under "Group", choose which of your categorical variables you want to use to define groups.
Under "Group 2", you may choose a second categorical variable for further analysis (optional)
Under "Compare 2", you may choose a second numerical variable for cases where you would like to explore two numerical variables (such as in Two-way MANOVA)
Several tests are available in the right margin. These tests are described below.
You can apply filters to the dataset to analyse subgroups (optional).
Export your results(Optional)
Shapiro-Wilk Test
Shapiro-Wilk Test is used to test for normal distribution. The null hypothesis is that the population is normally distributed. A p-value less than the chosen alpha level implies that the test data is not normally distributed and the assumptions for a parametric test are violated.
Activate the toggle switch beside "Shapiro-Wilk Test" in the right margin of the analysis card
The results (p-values) are shown in the last row of the table (named “Shapiro”).
Independent t-test
The test compares the means of two independent groups. (It is only available in cases where the categorical variable selected under "Group" consists of two values or where the dataset is filtered down to only two values). To run an independent t-test, "Compare" and "Group" must be defined.
Activate the toggle switch beside "Independent t-test" in the right margin of the analysis card
The result is shown beneath the table.
Assumptions: The test is parametric and assumes normality of the data and equality of variances. Use the Shapiro-Wilk test to test for normality. A standard independent t-test is performed if the variances between the groups are equal.
Mann-Whitney U test
The test compares the differences between two independent groups when the dependent variable is not normally distributed. It is considered a non-parametric alternative to the independent t-test when the assumptions of normality and equality of variances are not met. (The test is only available when the categorical variable selected under "Group" consists of two values or where the dataset is filtered down to two values).
Activate the toggle switch beside "Mann-Whitney U Test" in the right margin of the analysis card.
The result is shown beneath the table.
Assumptions: The dependent variable must be ordinal or continuous, and the groups must be independent. The distributions of the two groups must also have the same shape.
One-way ANOVA
The one-way analysis of variance (ANOVA) is used to compare the means of three or more independent groups. The null hypothesis is that there is no difference between the means of the groups.
To run a One-way ANOVA, "Compare" and "Group" must be defined. The variable set for "Group" should contain three or more independent groups.
Activate the toggle switch beside "One-way ANOVA" in the right margin of the analysis card
The result is shown beneath the table (f- and p-value)
If the test returns a statistically significant result, Tukey HSD can be used to determine which groups are statistically significantly different from each other.
Assumptions: The groups must be independent, and the dependent variable should be normally distributed in each group. However, the test tolerates violations of the normality assumption. There should also be homogeneity of the variances.
Tukey's HSD test
Tukey's Honest Significant Difference (HSD) test is a post hoc test used to assess the significance of differences between pairs of group means. The test determines which groups differ statistically significantly in means by comparing all possible pairs. The test should only be run after it has been shown that there is an overall statistically significant difference between the groups’ means.
Activate the toggle switch beside "Tukey's HSD" in the right margin of the analysis card
A table showing all the possible pairs and the p-values is shown at the bottom of the analysis card.
Kruskal-Wallis test
The Kruskal-Wallis test compares the median of two or more independent groups without assuming anything about the underlying distribution. The null hypothesis is that there is no difference between the groups' median.
To run the Kruskal-Wallis test, "Compare" and "Group" must be defined, and "Group" should contain three or more independent groups.
Activate the toggle switch beside “Kruskal-Wallis test” in the right margin of the analysis card.
The result is shown beneath the table.
If the test returns a statistically significant result, a Dunn`s test (not available yet) can be run. Also, a pair-wise Mann-Whitney test can be run to investigate differences between groups.
Assumptions: The groups must be independent, but there is no assumption regarding the data distribution within the groups.
Two-way ANOVA
The two-way analysis of variance (Two-way ANOVA) is used to compare the means of groups in two independent categorical values. It analyses the differences in mean within each of the variables and the interaction effect between the two independent variables.
To run Two-way ANOVA, "Compare" and "Group" must be chosen, and in addition, "Group 2" must contain the second categorical variable.
Activate the toggle switch beside “Two-way ANOVA” in the right margin of the analysis card
The result is shown beneath the table (f- and p-value) for each of the two categorical variables and for the interaction between the two.
Assumptions: The groups must be independent, and the dependent variable should be normally distributed in each group. There should also be homogeneity of the variances.
Significance can be followed up with a post hoc Tukey's test.
One-way MANOVA
The one-way multivariate analysis of variance (One-way MANOVA) is similar to one-way ANOVA, but adds the opportunity to include two dependent variables. The primary purpose of the one-way MANOVA is to understand if there is an interaction between the independent variable on the two (or more) dependent variables.
The One-way MANOVA requires that nine assumptions are fulfilled. These are:
The dependent variables should be continuous and numeric.
The independent variable should contain two or more independent groups.
The observations should be independent in and between the groups.
The number of samples in each group needs to be higher than the number of dependent variables.
There should not be any univariate or multivariate outliers. If in doubt, check by measuring the Mahalanobis distance.
There should be a linear relationship between each pair of dependent variables for all combinations of groups of independent variables. This can be tested by making scatter plots for all combinations.
There should be multivariate normality. This is an assumption that is difficult to test. However, normality for the dependent variables for each of the independent variables can be tested by Shapiro-Wilks.
There is homogeneity of variance-covariance matrices. The use of other software is needed to test this assumption.
There is no multicollinearity. The dependent variables should have low to moderate correlations with each other, but not high (>0.9). If so, use one-way ANOVA.
If these assumptions are not met, the One-way MANOVA might not be valid.
To run a One-way MANOVA, the two dependent variables are entered into "Compare" and "Compare 2", and "Group" must be defined for the categorical variable.
Activate the toggle switch beside “One-way MANOVA” in the right margin of the analysis card
The result is shown beneath the table in a complex matrix.
Two-way MANOVA
The two-way multivariate analysis of variance (two-way MANOVA) is similar to two-way ANOVA, but adds the opportunity to include two dependent variables. The primary purpose of the two-way MANOVA is to understand if there is an interaction between the two independent variables on the two (or more) dependent variables.
The two-way MANOVA requires that nine assumptions are fulfilled. These are:
The dependent variables should be continuous and numeric.
The independent variables should contain two or more independent groups.
The observations should be independent in and between the groups.
The number of samples in each group needs to be higher than the number of dependent variables.
There should not be any univariate or multivariate outliers. If in doubt, check by measuring the Mahalanobis distance.
There should be a linear relationship between each pair of dependent variables for all combinations of groups of independent variables. This can be tested by making scatter plots for all combinations.
There should be multivariate normality. This is an assumption that is difficult to test. However, normality for the dependent variables for each of the independent variables can be tested by Shapiro-Wilks.
There is homogeneity of variance-covariance matrices. The use of other software is needed to test this assumption.
There is no multicollinearity. The dependent variables should have low to moderate correlations with each other, but not high (>0.9). If so, use one-way ANOVA.
If these assumptions are not met, the Two-way MANOVA might not be valid.
To run a two-way MANOVA, the two dependent variables are entered into "Compare" and "Compare 2", and both "Group" and "Group 2" must be defined for categorical variables.
Activate the toggle switch beside “Two-way MANOVA” in the right margin of the analysis card
The result is shown beneath the table in a complex matrix.