# Statistical Tests – Explanation of the Different Types & Examples

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Statistical tests are used in probability research. They are used by researchers to confirm whether a data set sufficiently supports the hypothesis of the study.

A hypothesis refers to a phenomenon or scientific observation to be tested further using statistical tests.

## Statistical Test – In a Nutshell

• Statistical sets are an essential tool in research.
• They are used to test the differences between variables in a data set to determine causality and correlation.
• There are different types of statistical sets for the various types of data used for research.

## Definition: Statistical tests

Statistics is the science of gathering, organizing, summarizing, and analyzing data in the interest of a research problem. Statistical tests are one of the tools used to assert if an input variable has a statistical effect on a resultant variable. They are also deployed to determine the difference between two or more classes.1

Statistical tests further assume the null hypothesis, which states that there are no differences between two populations or classes. Two possibilities are the same, and any significant, observable differences are purely by chance or error.2

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## Purpose of statistical tests

Statistical tests begin by estimating a test statistic. The test statistic measures the variation between the variables in a test and the null hypothesis, where no differences exist.

Statisticians then calculate the p-value. It is a statistical measurement that compares a proposed hypothesis with observable characteristics in the data set.3

The p-value estimates the likelihood of arriving at the observable outcomes if the null hypothesis is true.

A less extreme difference between the test and null hypothesis statistic implies no significant relationship between the input and outcome variables.

On the other hand, if the difference is more extreme, the conclusion is a statistically significant relationship between the input and outcome variables.4

## Performing statistical tests

Statistical tests require a large sample size to determine the accurate distribution in the population postulated for research. Data for statistical tests can be collected from experiments or probability samples obtained from observations.

Researchers may use different types of statistical tests depending on:

• How the data meets defined assumptions
• The types of variables present

### Statistical Assumptions

Statistical tests assume the following conditions:

 No autocorrelation/Independent observations The variables in the test should not be related; for instance, different test subjects are independent. The observations in one sample should be different from the next. Homogeneity of variances In a test case, the variance within one group should be similar across other groups. Variations in variances reduce the accuracy of a statistical test. Normality The data in a quantitative statistical test should exhibit the pattern of a normal distribution curve.5

However, you may encounter data sets that fail to meet one or more of these assumptions. You can perform other tests in this case.

For instance, nonparametric statistical tests are used when there is no homogeneity or normality in the data. Repeated measured tests can be conducted where the data lacks independent variables.

### Types of variables

Different statistical tests are best suited for different types of variables. Some of the variables include:

#### Quantitative variables

These are numerically measurable variables, such as the number of cars in a lot.

Quantitative variables can be further classified into:

• Continuous variables: Also known as ratio variables. These are units of measurement that can be represented in quantities less than 1. For instance, 0.8 km.
• Discrete or integer variables: Units that cannot be divided, such as 1 car or 1 tree.6

#### Categorical variables

They describe classes or groups of things, for instance, the models of a vehicle.

Categorical variables are divided into the following variables:

• Binary: Data that has one of two outcomes, such as yes/no or pass/fail
• Nominal: Used to describe data with no intrinsic order, such as brands, families, species
• Ordinal: For ordered data types with observable scales of hierarchy, such as user ratings.7

## Statistical tests: Parametric test

Parametric tests are used in samples that exhibit a normal distribution, among other statistical assumptions. They use these assumptions to control the sample distribution to achieve stronger conclusions compared to nonparametric tests.

Parametric tests include:

### Regression tests

They measure the relationship between two variables for causality and effect. Regression tests in statistical contexts include simple linear, multiple linear, and logistic regressions.8

### Comparison tests

These tests evaluate the difference between group averages. They determine the effect of a given variable on the mean value of other variables.

T-tests

• Used to compare the averages in two groups, for instance, the mean age of boys and girls in a class.

ANOVA

• A statistical test to determine statistical differences in the mean of more than two independent groups.

MANOVA

• It is used where there is more than one variable used to determine the mean differences in three or more independent groups.

Example t-test:

• What is the difference in terms of the final grade point average for students from two different schools?

Example ANOVA:

• What is the difference in average speed among drivers given three different car makes?

Example MANOVA:

• What is the effect of pop culture on behavior, social skills, and personality?9

### Correlation tests

Correlation tests determine the relationship between two variables without proposing a cause-effect relationship. They can be used in multiple regression to test if there is autocorrelation between two variables.

Example:

How are temperature and rainfall related?

## Statistical tests: Nonparametric test

Nonparametric tests don’t require any underlying assumptions in the research data. They are applied when a sample fails to follow acceptable statistic assumptions.

Nonparametric tests are, however, not considered as strong as parametric evaluations.

Types of nonparametric tests:

• Spearman’s r
• Chi-square test of independence
• Sign test
• Kruskal-Wallis H
• ANOSIM
• Wilcoxon rank-sum test
• Wilcoxon signed-rank test

## Choosing a statistical test: Flowchart

The following flowchart allows you to choose the correct statistical test for your research easily.

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#### What is a test statistic?

A test statistic is a unit or quantity calculated from a sample in research. Test statistics are used as an evaluative metric in analysis for hypothesis testing.

#### Can I use statistical tests?

Statistical tests are used to test and determine the differences between two variables, i.e., the predictive and output variables in a study. The tests always assume a null hypothesis between two samples.

#### What is the difference between parametric and nonparametric tests?

Parametric tests are where there are observable statistical distributions in a data set. Nonparametric tests do not consider any distributions and do not consider statistical assumptions.

#### Why do we perform statistical tests?

Statistical tests are applied to study research problems with several variables. Researchers do statistical tests to see how different variables interact and how much they affect each other.

#### What are the statistical assumptions?

The statistical assumptions used in statistical tests are independent observations, normality, and homogeneity. Nonparametric tests are used if one or more of these conditions is missing in a data sample.

## Sources

1 Clinical Pharmacology & Public Health. “An Introduction to Statistical Tests.” 2015. Educational video, 32:50. https://www.youtube.com/watch?v=f6Ej1tAV5GA.

2 OxfordLanguages. “Oxford Languages and Google.” Accessed on November 04, 2022. https://languages.oup.com/google-dictionary-en/.

3 NIST. “What are statistical tests?.” Accessed on November 04, 2022. https://www.itl.nist.gov/div898/handbook/prc/section1/prc13.htm.

4 Beers, Brian. “P-Value: What It Is, How to Calculate It, and Why It Matters.” Investopedia. May 18, 2022. https://www.investopedia.com/terms/p/p-value.asp.

5 Statistics Solutions. “Common Assumptions in Statistics.” Accessed November 04, 2022. https://www.statisticssolutions.com/common-assumptions-in-statistics/.

6 Glen, Stephanie. “Quantitative Variables (Numeric Variables): Definition, Examples.” Statistics How To. Accessed November 04, 2022.  https://www.statisticshowto.com/quantitative-variables-data/.

7 UCLA: Statistical Consulting Group. “What is the difference between categorical, ordinal and interval variables?.” Accessed November 04, 2022. https://stats.oarc.ucla.edu/other/mult-pkg/whatstat/what-is-the-difference-between-categorical-ordinal-and-interval-variables/.

8 Alchemer. “What is Regression Analysis and Why Should I Use It?.” Accessed November 04, 2022. https://www.alchemer.com/resources/blog/regression-analysis/.

9 Frost, Jim. “Multivariate ANOVA (MANOVA) Benefits and When to Use It.” Statistics By Jim. Accessed November 04, 2022. https://statisticsbyjim.com/anova/multivariate-anova-manova-benefits-use/.

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