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

### Table of Contents

- What test to use if data is not normally distributed?
- Do you need normality for t-test?
- What should I do if my data is not normally distributed?
- Are t tests robust to non-normality?
- Can we use Anova for non normal data?
- Can you standardize non normal data?
- Can I use t-test for skewed data?
- What are the limitations of the t-test?
- Can we use Anova for non-normal data?
- Is t-test a nonparametric test?
- When to use t tests?
- What are the limitations of t test?
- What assumptions are made when conducting a t-test?
- What are the conditions for t test?

### 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 Data | Equivalent Tools for Non-Normally Distributed Data |

ANOVA | Mood's median test; Kruskal-Wallis test |

Paired t-test | One-sample sign test |

F-test; Bartlett's test | Levene'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** [75] and performing better with large sample sizes [79] . 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 test | 1-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.