What Statistical Test to Use When Comparing Two Means
Choosing the Right Statistical Test | Types and Examples
Statistical tests are used in hypothesis testing. They can be used to:
- determine whether a predictor variable has a statistically significant relationship with an issue variable.
- judge the divergence between two or more groups.
Statistical tests assume a null hypothesis of no human relationship or no departure between groups. Then they make up one's mind whether the observed data fall exterior of the range of values predicted by the null hypothesis.
If you already know what types of variables you're dealing with, yous tin utilize the flowchart to choose the correct statistical test for your data.
Statistical tests flowchart
What does a statistical test practise?
Statistical tests piece of work by computing a test statistic – a number that describes how much the human relationship betwixt variables in your exam differs from the nada hypothesis of no relationship.
It then calculates a p-value (probability value). The p-value estimates how probable information technology is that you would see the difference described by the examination statistic if the zip hypothesis of no relationship were true.
If the value of the test statistic is more than extreme than the statistic calculated from the zip hypothesis, then you can infer a statistically significant human relationship between the predictor and outcome variables.
If the value of the exam statistic is less extreme than the one calculated from the zilch hypothesis, so y'all tin infer no statistically significant relationship between the predictor and outcome variables.
When to perform a statistical test
You lot tin perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment, or through observations made using probability sampling methods.
For a statistical examination to be valid, your sample size needs to be large plenty to approximate the true distribution of the population existence studied.
To determine which statistical test to use, you lot need to know:
- whether your data meets certain assumptions.
- the types of variables that yous're dealing with.
Statistical assumptions
Statistical tests make some mutual assumptions about the data they are testing:
- Independence of observations (a.yard.a. no autocorrelation): The observations/variables you include in your examination are not related (for case, multiple measurements of a unmarried test subject area are non independent, while measurements of multiple unlike test subjects are contained).
- Homogeneity of variance: the variance within each grouping being compared is similar amidst all groups. If ane group has much more variation than others, it will limit the test's effectiveness.
- Normality of data: the data follows a normal distribution (a.m.a. a bell bend). This supposition applies only to quantitative data.
If your data practise not meet the assumptions of normality or homogeneity of variance, you lot may be able to perform a nonparametric statistical examination, which allows you to brand comparisons without whatever assumptions about the data distribution.
If your data practise non come across the supposition of independence of observations, y'all may exist able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).
Types of variables
The types of variables you have usually determine what type of statistical exam you can use.
Quantitative variables represent amounts of things (eastward.g. the number of trees in a forest). Types of quantitative variables include:
- Continuous (a.k.a ratio variables): correspond measures and can usually be divided into units smaller than one (e.1000. 0.75 grams).
- Discrete (a.k.a integer variables): correspond counts and usually can't exist divided into units smaller than one (eastward.grand. 1 tree).
Categorical variables represent groupings of things (e.thou. the dissimilar tree species in a forest). Types of chiselled variables include:
- Ordinal: represent data with an social club (e.grand. rankings).
- Nominal: stand for group names (due east.yard. brands or species names).
- Binary: represent information with a yes/no or one/0 outcome (due east.one thousand. win or lose).
Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment, these are the contained and dependent variables). Consult the tables beneath to see which exam best matches your variables.
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Choosing a parametric test: regression, comparison, or correlation
Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.
The virtually common types of parametric exam include regression tests, comparing tests, and correlation tests.
Regression tests
Regression tests look for crusade-and-effect relationships. They can be used to estimate the effect of 1 or more continuous variables on another variable.
| Predictor variable | Outcome variable | Research question example | |
|---|---|---|---|
| Uncomplicated linear regression |
|
| What is the result of income on longevity? |
| Multiple linear regression |
|
| What is the upshot of income and minutes of exercise per solar day on longevity? |
| Logistic regression |
|
| What is the effect of drug dosage on the survival of a examination subject? |
Comparison tests
Comparison tests look for differences among group means. They tin can exist used to examination the effect of a categorical variable on the mean value of some other characteristic.
T-tests are used when comparing the ways of precisely two groups (e.grand. the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (due east.m. the average heights of children, teenagers, and adults).
| Predictor variable | Outcome variable | Research question instance | |
|---|---|---|---|
| Paired t-test |
|
| What is the result of two different exam prep programs on the average exam scores for students from the aforementioned form? |
| Contained t-test |
|
| What is the difference in average exam scores for students from two unlike schools? |
| ANOVA |
|
| What is the difference in average pain levels among mail-surgical patients given three different painkillers? |
| MANOVA |
|
| What is the effect of blossom species on petal length, petal width, and stem length? |
Correlation tests
Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.
These can be used to exam whether two variables you lot desire to use in (for case) a multiple regression test are autocorrelated.
| Variables | Research question example | |
|---|---|---|
| Pearson'due southr |
| How are latitude and temperature related? |
Choosing a nonparametric test
Non-parametric tests don't make as many assumptions about the information, and are useful when ane or more of the mutual statistical assumptions are violated. Even so, the inferences they make aren't every bit strong as with parametric tests.
| Predictor variable | Outcome variable | Use in place of… | |
|---|---|---|---|
| Spearman'sr |
|
| Pearson'southwardr |
| Chi foursquare examination of independence |
|
| Pearson'sr |
| Sign test |
|
| One-sample t-test |
| Kruskal–WallisH |
|
| ANOVA |
| ANOSIM |
|
| MANOVA |
| Wilcoxon Rank-Sum test |
|
| Independent t-test |
| Wilcoxon Signed-rank examination |
|
| Paired t-test |
Flowchart: choosing a statistical exam
This flowchart helps yous cull among parametric tests. For nonparametric alternatives, check the table above.
Often asked questions most statistical tests
- What is a test statistic?
-
A examination statistic is a number calculated by a statistical examination. It describes how far your observed information is from the zilch hypothesis of no relationship betwixt variables or no departure among sample groups.
The test statistic tells you how different ii or more groups are from the overall population hateful, or how different a linear slope is from the slope predicted by a null hypothesis. Different test statistics are used in different statistical tests.
- What is statistical significance?
-
Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the goose egg hypothesis of a statistical exam. Significance is unremarkably denoted by a p-value, or probability value.
Statistical significance is arbitrary – it depends on the threshold, or alpha value, called by the researcher. The most common threshold is p < 0.05, which means that the information is likely to occur less than 5% of the fourth dimension under the null hypothesis.
When the p-value falls beneath the called alpha value, then we say the result of the test is statistically pregnant.
- What is the difference between quantitative and categorical variables?
-
Quantitative variables are whatever variables where the data correspond amounts (eastward.g. height, weight, or age).
Categorical variables are any variables where the data correspond groups. This includes rankings (e.yard. finishing places in a race), classifications (due east.m. brands of cereal), and binary outcomes (e.g. coin flips).
You lot need to know what type of variables y'all are working with to choose the right statistical test for your data and interpret your results.
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