# What test to use if data is not normally distributed? ### What test to use if data is not normally distributed?

No Normality Required
Comparison of Statistical Analysis Tools for Normally and Non-Normally Distributed Data
Tools for Normally Distributed DataEquivalent Tools for Non-Normally Distributed Data
ANOVAMood's median test; Kruskal-Wallis test
Paired t-testOne-sample sign test
F-test; Bartlett's testLevene's test

### Do you need normality for t-test?

The independent t-test requires that the dependent variable is approximately normally distributed within each group. ... However, the t-test is described as a robust test with respect to the assumption of normality. This means that some deviation away from normality does not have a large influence on Type I error rates.

### What should I do if my data is not normally distributed?

Many practitioners suggest that if your data are not normal, you should do a nonparametric version of the test, which does not assume normality. From my experience, I would say that if you have non-normal data, you may look at the nonparametric version of the test you are interested in running.

### Are t tests robust to non-normality?

the t-test is robust against non-normality; this test is in doubt only when there can be serious outliers (long-tailed distributions – note the finite variance assumption); or when sample sizes are small and distributions are far from normal. 10 / 20 Page 20 . . .

### Can we use Anova for non normal data?

The one-way ANOVA is considered a robust test against the normality assumption. ... As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate.

### Can you standardize non normal data?

1 Answer. The short answer: yes, you do need to worry about your data's distribution not being normal, because standardization does not transform the underlying distribution structure of the data. If X∼N(μ,σ2) then you can transform this to a standard normal by standardizing: Y:=(X−μ)/σ∼N(0,1).

### Can I use t-test for skewed data?

For studies with a large sample size, t-tests and their corresponding confidence intervals can and should be used even for heavily skewed data.

### What are the limitations of the t-test?

Test limitations include sensitivity to sample sizes, being less robust to violations of the equal variance and normality assumptions when sample sizes are unequal  and performing better with large sample sizes  . T-tests were used in our study to compare means between groups for continuous variables. ...

### Can we use Anova for non-normal data?

The one-way ANOVA is considered a robust test against the normality assumption. ... As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate.

### Is t-test a nonparametric test?

Nonparametric tests are also called distribution-free tests because they don't assume that your data follow a specific distribution....Hypothesis Tests of the Mean and Median.
Parametric tests (means)Nonparametric tests (medians)
1-sample t test1-sample Sign, 1-sample Wilcoxon

### When to use t tests?

• A t-test can be used to compare two means or proportions. The t-test is appropriate when all you want to do is to compare means, and when its assumptions are met (see below). In addition, a t-test is only appropriate when the mean is an appropriate when the means (or proportions) are good measures.

### What are the limitations of t test?

• Limitations of the t-Test. Testing differences between group means. – IV: Gender (Male & Female) – IV: High-school class (First-year, Sophomore, Junior, & Senior) – Using the t-Test, we must either “collapse” categories… or not run the analysis. Limitations of the t-Test. 1 Independent Variable.

### What assumptions are made when conducting a t-test?

• The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation.

### What are the conditions for t test?

• One of the important conditions for adopting t-test is that population variance is unknown. Conversely, population variance should be known or assumed to be known in case of a z-test. Z-test is used to when the sample size is large, i.e. n > 30, and t-test is appropriate when the size of the sample is small, in the sense that n < 30.