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MindMap Gallery statistical tests

statistical tests

This is a mind map about statistical testing, including normality, non-normality, etc. Hope this helps!

Edited at 2023-11-11 11:22:03

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Outline

Does it conform to normal distribution?

consistent with normal

Parametric test Refers to statistical testing of parameters such as mean and variance of sample data

Regression coefficient test Used to test the causal relationship between variables in sample data, that is, whether the independent variable has a significant impact on the dependent variable

simple linear regression

The independent variable and the dependent variable are each a quantitative variable, such as what impact does income have on longevity?

Multiple Regression

Independent variable: two or more continuous quantitative variables, dependent variable: one quantitative variable; such as the impact of income and daily exercise time on longevity

logistic regression

Independent variables: quantitative variables, dependent variables: qualitative variables; such as the impact of drug dosage on the survival of subjects

comparative test Find differences between group means. Can be used to examine/test the impact of qualitative (categorical) variables on the means of other features.

T test It is used for normally distributed data with a small sample size (for example, n<30), where the data to be compared is required to obey a normal distribution, and the overall standard deviation σ is unknown. The t test can only be used to compare two sample means and the sample mean and the population mean.

Independent samples T-test

Independent variable: A qualitative (categorical) variable that compares two groups. Dependent variable: A quantitative variable from two groups of different populations. Used to compare the difference in means between two independent samples. In this case, there are two independent sets of sample data, such as a comparison of the effects of two different treatment methods. The T-test will calculate the difference in means between two groups of samples and evaluate whether this difference is significant.

Paired samples T-test

Independent variable: A qualitative (categorical) variable. Dependent variable: A quantitative variable from two different groups of the same population. Used to compare the mean differences of the same group of samples under different conditions. In this case there are two related samples of the same group of individuals, for example measurements taken before and after treatment. The paired samples T-test will calculate the difference between each pair of samples and evaluate whether the difference is significant.

One-sample T-test

Used to compare the difference between the mean of a sample and a known mean. In this case there is a sample data and a known reference mean, such as in some drug efficacy evaluation, the sample mean is compared to the known average treatment effect. The one-sample t-test will calculate the difference between the sample mean and the reference mean and evaluate whether this difference is significant.

Analysis of Variance (ANOVA)

Independent variable: one or more qualitative (categorical) variables. Dependent variable: A quantitative variable. What is the difference in pain levels among patients taking three different analgesics after surgery?

Multivariate Analysis of Variance (MANOVA)

Independent variable: one or more qualitative (categorical) variables. Dependent variable: two or more quantitative variables. What effect does flower type have on petal length, petal width, and stem length?

Z test This method is generally used to test the difference in mean values of large samples (that is, the sample size is greater than 30). It uses the theory of standard normal distribution to judge the probability of difference, and then compares whether the difference between two averages > average is significant.

F test Also called homogeneity of variance test. The F test is used in the two-sample t-test. Determining whether the variances of the two populations are equal is a prerequisite for choosing which T test (two-sample test with equal variances or two-sample test with heteroscedasticity)

correlation test Test whether two quantitative variables are related without assuming causality

Pearson's r

Independent variable: continuous quantitative variable, dependent variable: continuous quantitative variable; what is the relationship between dimensions and temperature?

r: positive correlation negative correlation

U test

Not consistent with normality

Non-parametric test The overall distribution is difficult to determine, or the distribution is obviously skewed, the variance is uneven, and there is no appropriate variable conversion method.

Chi-square test (chi-square) Test whether there is a relationship between categorical variables SPSS: analyze-descriptive-crosstabs

Frequency comparison of dichotomous variables between two groups. Such as traditional Chinese medicine and western medicine treatment, the number of effective and ineffective. Using Pearson chi-square for large samples

r: correlation strength, there is no positive or negative correlation, only correlation strength

Frequency comparison of multiple groups of categorical variables Pearson chi-square

MacNemar

Paired samples Categorical variable frequency comparison

Fisher test

Same usage scenario as chi-square test, but suitable for small samples

Spearman correlation coefficient

Independent variable: quantitative variable, dependent variable: quantitative variable

Alternative parametric test method: Pearson's r

sign check

Independent variable: three or more groups of qualitative categorical variables, dependent variable: quantitative variable

Alternative parametric test method: one-sample T-test

Kruskal-Wallis H test

multiple independent samples Independent variable: three or more groups of qualitative categorical variables, dependent variable: quantitative variable

Alternative Parametric Testing Method: Analysis of Variance

ANOSIM

Independent variable: three or more groups of qualitative categorical variables, dependent variable: two or more quantitative variables

Alternative Parametric Test Method: Multivariate Analysis of Variance

Wilcoxon rank sum test

Independent variables: two sets of qualitative categorical variables, dependent variables: quantitative variables from different population sample groups

Alternative parametric test method: independent samples T-test

Level data, frequencies of different levels.

signed rank test (Wilcoxon signed rank test)

Independent variable: two sets of qualitative categorical variables, dependent variable: quantitative variable of different sample groups from the same population

Alternative parametric test method: paired samples T test