Parametric vs Non-Parametric Tests

What are the assumptions of a parametric test?

normal distribution, homogeneity of variance, and independence

What are some examples of parametric tests?

t-test, ANOVA, and Pearson correlation

When should non parametric tests be used?

When data is not normally distributed, if the sample size is small, when using ordinal or nominal data, and if there is outliers

What are some examples of non parametric tests?

Mann-Whitney U test, Wilcoxon signed-rank test, Kristal-Wallis test, and Spearman's rank correlation

What type of test is more powerful?

When the assumption are met, parametric tests are more powerful

What does it mean when we ask about the power of a test?

The power means that the test is more likely to detect a statistically significant effect if there is one. Higher power correlates to lower risk of type II errors

What does a violation of the assumption of normality mean for the statistics?

Violation of this assumption can lead to inaccurate p values and incorrect conclusions

What is homogeneity of variance or homoscedasticity?

The variance of the data is equal across different groups being compared

What does a violation of the assumption of homogeneity mean for the statistics?

Unequal variances can inflate type I error or false positive rates

What does independence of observations mean?

Each data point is independent of the others, meaning that one observation does not influence another

What type of data is assumed to be used in a parametric test?

interval or ratio data

What are the different types of t tests?

independent samples or independent sample t-tests, paired samples or dependent sample t-tests, and one sample t-test

What does ANOVA stand for?

Analysis of variance

What is ANOVA used for?

Used to compare the means of three or more groups

What is one weakness of ANOVA tests?

They do not show which groups are statistically different from one another

What does the Pearson correlation do?

measures the linear relationship between two continuous variables

What does the regression analysis do?

predicts the value of a dependent variable based on the values of independent variables while relying on parametric assumptions

What are the advantages of parametric test?

They are more powerful, more versatile, and easier to interpret

What are some disadvantages of parametric tests?

They require strict assumptions and they are sensitive to outliers

What are data transformations?

If the data is not normally distributed, it may be possible to transform the data to achieve normality

What are non-parametric tests?

Tests that do not test hypotheses concerning parameters, and do not assume the population is normally distributed

What is another name for non parametric tests?

distribution-free tests

What are some advantages to non parametric test?

They require fewer assumptions, are more robust to outliers, and are suitable for non normal data

What type of data can non parametric tests be used for?

ordinal and nominal data

What are some disadvantages to non parametric tests?

They have lower power and often provide less detailed information about the data

If you have interval or ratio data with a large sample size what type of test should you use?

parametric tests, but be aware of outliers and any violations to normality

If you have interval or ratio data, a small sample size and data that is not normally distributed, what type of test should you use?

non parametric because the data is not normally distributed

What is the parametric test that should be used when you have one sample?

one sample t-test

What is the parametric test that should be used when you have two independent groups?

Independent t-test or two sample t-test

What parametric tests should be used when you have two paired groups?

paired t-test or dependent t-test

What parametric test should be used when you have three or more groups?

one way ANOVA

What non parametric test should be used when you have one sample?

Wilcoxon signed-rank

What non parametric test should be used when you have two independent groups?

Mann-Whitney U test

What non parametric test should be used when you have two paired groups?

Wilcoxon signed-rank

What non parametric test should be used when you have th?ree or more groups?

Kruskal-Wallis H test

What is the difference between practical and statistical significance?

A statistically significant result does not necessarily meant that the result is meaningful in the real world?

Non parametric tests sacrifice some ___ for more ___

power, robustness

ANOVA is an ___ of t-test that allows us to test ___ comparisons with one test

expansion, many

How does ANOVA control the type I error rate?

by testing all groups simultaneously with a single F-test

What is the first step of using an ANOVA?

Determining if there might be any differences among the means of the groups

What is the second step of using an ANOVA?

If the p value is below the stated significance value then a second step is required to determine which groups differ from the others using pothoc tests such as Tukey's HSD test

T/F: A second step is ALWAYS needed when it comes to using an ANOVA

FALSE; a second step is only needed if the p value is below the stated significance level

When is a one way ANOVA applied?

In single factor studies when three or more independent group means are compared

What does "one-way" indicate?

It indicates that the design involves one independent variable with three or more levels

What are the assumptions for ANOVA?

Independence, normality, homogeneity of variance, and interval scale of data

What is statistical independence?

The probability of one event occurring does not affect the probability of another event occurring

What does "two-way" denote?

The study design involved two independent variables with three or more levels

ANOVA is generally robust to mild violations of ____ when sample sizes are ___

homogeneity of variance, equal

When is ANOVA not as robust to violations in homogeneity of variance?

When group sizes are unequal, especially when small sample sizes have large variances

What alternatives can be used for ANOVA when there's significant violations to homogeneity in variance?

Kuskal-Wallis test