Kruskal-Wallis H test.
ratio
Ordinal. Tests responses are usually correct or incorrect. This would be assigned a value and the number of correct answers is the score of the test. There is a logical order, a correct answer is better than an incorrect answer, so it is not nominal data. Even though we calculate averages, test responses are not interval data, as there is no meaning to the interval. See related link.
To test a prediction based on one of two hypotheses.
A powerful test is the chi-square contingency table.
The two samples must be independent and the data must be at least ordinal. Under those conditions the Mann-Whitney U test can be used.
ratio
Ordinal data, which represents ordered categories, can be analyzed using several statistical methods. Descriptive statistics, such as median and mode, are commonly used to summarize the data. For inferential analysis, non-parametric tests like the Mann-Whitney U test or Kruskal-Wallis test can be applied, as they do not assume normal distribution. Additionally, techniques like ordinal logistic regression can model relationships while respecting the ordinal nature of the data.
The independent variable in ANOVA must be categorical (either nominal or ordinal). The dependent variable must be scale (either interval or ratio). However, it is possible to recode scale variables to categorical and vice versa in order to perform ANOVA. While this is a common practice in many social sciences, it is controversial. I have also seen studies where ordinal data is treated as scale in ANOVA. Personally, I do not endorse either practice as they are tailoring the data to fit the test instead of the proper method of selecting a test that fits the data.
Ordinal. Tests responses are usually correct or incorrect. This would be assigned a value and the number of correct answers is the score of the test. There is a logical order, a correct answer is better than an incorrect answer, so it is not nominal data. Even though we calculate averages, test responses are not interval data, as there is no meaning to the interval. See related link.
To determine the correct statistical test for a research study, first identify the type of data you have (e.g., nominal, ordinal, interval, or ratio) and the research question you aim to address. Next, consider the number of groups being compared (e.g., one-sample, two-sample, or multiple groups) and whether the data meets assumptions like normality and homogeneity of variance. Finally, match your study design (e.g., independent vs. paired samples) with appropriate tests, such as t-tests for comparisons of means or chi-square tests for categorical data.
A non-parametric test is a type of statistical test that does not assume a specific distribution for the data, making it suitable for analyzing data that may not meet the assumptions of parametric tests. These tests are often used for ordinal data or when sample sizes are small. Common examples include the Mann-Whitney U test and the Kruskal-Wallis test. Non-parametric tests are typically more robust to outliers and can be applied to a wider range of data types.
statistical goodness of fit test used for categorical data to test if a sample of data came from a population with a specific distribution. It can be applied for discrete distributions.
To test a prediction based on one of two hypotheses.
A powerful test is the chi-square contingency table.
Non-parametric statistical tests are designed for rank data when the assumptions required for parametric tests (such as normality and homogeneity of variance) are not met. These tests rely on the relative ordering of the data rather than their specific values, making them suitable for ordinal data or when sample sizes are small. Examples include the Wilcoxon signed-rank test and the Kruskal-Wallis test, which are used to compare medians across groups. By focusing on ranks, these methods provide more robust analyses in the presence of outliers or non-normal distributions.
Parametric statistical tests assume that your data are normally distributed (follow a classic bell-shaped curve). An example of a parametric statistical test is the Student's t-test.Non-parametric tests make no such assumption. An example of a non-parametric statistical test is the Sign Test.
It depends on what you want to test. Goodnesss of fit or some null hypothesis?