N Order to Select the Appropriate Statistical Tool to Analyze Quantitative Data You First Must Know
Choosing the Right Statistical Examination | 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 outcome variable.
- approximate the difference between ii or more groups.
Statistical tests assume a nada hypothesis of no relationship or no divergence between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.
If you already know what types of variables you lot're dealing with, yous can use the flowchart to choose the correct statistical test for your data.
Statistical tests flowchart
What does a statistical test exercise?
Statistical tests piece of work by computing a test statistic – a number that describes how much the human relationship betwixt variables in your test differs from the null hypothesis of no human relationship.
It then calculates a p-value (probability value). The p-value estimates how likely it is that you would see the deviation described by the test statistic if the aught hypothesis of no relationship were truthful.
If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.
If the value of the test statistic is less farthermost than the one calculated from the null hypothesis, and then you tin can infer no statistically significant relationship between the predictor and outcome variables.
When to perform a statistical test
You can perform statistical tests on data that take been collected in a statistically valid manner – either through an experiment, or through observations made using probability sampling methods.
For a statistical test to be valid, your sample size needs to be large enough to approximate the true distribution of the population being studied.
To determine which statistical test to use, you need to know:
- whether your information meets sure assumptions.
- the types of variables that y'all're dealing with.
Statistical assumptions
Statistical tests make some mutual assumptions about the data they are testing:
- Independence of observations (a.m.a. no autocorrelation): The observations/variables you include in your examination are non related (for example, multiple measurements of a single test subject area are non contained, while measurements of multiple dissimilar test subjects are independent).
- Homogeneity of variance: the variance inside each group existence compared is similar amongst all groups. If 1 group has much more variation than others, information technology volition limit the test's effectiveness.
- Normality of data: the data follows a normal distribution (a.chiliad.a. a bell curve). This assumption applies only to quantitative data.
If your information practise not meet the assumptions of normality or homogeneity of variance, you lot may be able to perform a nonparametric statistical exam, which allows y'all to make comparisons without any assumptions nearly the data distribution.
If your information practice not meet the assumption of independence of observations, you may be able to use a exam that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).
Types of variables
The types of variables you lot accept commonly determine what blazon of statistical exam you can use.
Quantitative variables correspond amounts of things (e.thousand. the number of trees in a forest). Types of quantitative variables include:
- Continuous (a.g.a ratio variables): represent measures and can unremarkably be divided into units smaller than 1 (e.g. 0.75 grams).
- Discrete (a.k.a integer variables): represent counts and commonly tin't be divided into units smaller than one (e.one thousand. 1 tree).
Categorical variables represent groupings of things (east.g. the unlike tree species in a forest). Types of chiselled variables include:
- Ordinal: correspond data with an order (e.one thousand. rankings).
- Nominal: represent group names (e.g. brands or species names).
- Binary: represent data with a yes/no or one/0 outcome (e.1000. win or lose).
Cull the test that fits the types of predictor and outcome variables y'all have nerveless (if you lot are doing an experiment, these are the contained and dependent variables). Consult the tables beneath to run into which exam best matches your variables.
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See an instance
Choosing a parametric examination: 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 most common types of parametric test include regression tests, comparison tests, and correlation tests.
Regression tests
Regression tests look for crusade-and-effect relationships. They tin can be used to estimate the effect of ane or more continuous variables on another variable.
| Predictor variable | Outcome variable | Enquiry question example | |
|---|---|---|---|
| Uncomplicated linear regression |
|
| What is the effect of income on longevity? |
| Multiple linear regression |
|
| What is the result of income and minutes of practice per day on longevity? |
| Logistic regression |
|
| What is the effect of drug dosage on the survival of a test subject field? |
Comparison tests
Comparison tests wait for differences among group means. They can be used to test the effect of a chiselled variable on the mean value of some other characteristic.
T-tests are used when comparing the means of precisely two groups (e.g. the boilerplate heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more ii groups (e.thousand. the average heights of children, teenagers, and adults).
| Predictor variable | Outcome variable | Inquiry question example | |
|---|---|---|---|
| Paired t-examination |
|
| What is the effect of two different test prep programs on the average examination scores for students from the same class? |
| Contained t-examination |
|
| What is the difference in average test scores for students from two different schools? |
| ANOVA |
|
| What is the difference in average hurting levels amidst mail-surgical patients given three different painkillers? |
| MANOVA |
|
| What is the effect of flower species on petal length, petal width, and stem length? |
Correlation tests
Correlation tests check whether variables are related without hypothesizing a crusade-and-effect relationship.
These can be used to test whether 2 variables you desire to use in (for example) a multiple regression test are autocorrelated.
| Variables | Research question example | |
|---|---|---|
| Pearson'southwardr |
| How are breadth and temperature related? |
Choosing a nonparametric test
Non-parametric tests don't make as many assumptions near the data, and are useful when one or more of the mutual statistical assumptions are violated. Even so, the inferences they make aren't equally strong as with parametric tests.
| Predictor variable | Event variable | Employ in identify of… | |
|---|---|---|---|
| Spearman'sr |
|
| Pearson'sr |
| Chi square test of independence |
|
| Pearson'sr |
| Sign test |
|
| Ane-sample t-test |
| Kruskal–WallisH |
|
| ANOVA |
| ANOSIM |
|
| MANOVA |
| Wilcoxon Rank-Sum exam |
|
| Contained t-examination |
| Wilcoxon Signed-rank test |
|
| Paired t-test |
Flowchart: choosing a statistical test
This flowchart helps you choose amidst parametric tests. For nonparametric alternatives, check the tabular array above.
Oft asked questions about statistical tests
- What is a exam statistic?
-
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship betwixt variables or no divergence amidst sample groups.
The test statistic tells you lot how different two or more than groups are from the overall population mean, or how dissimilar a linear slope is from the slope predicted past a cipher hypothesis. Different exam statistics are used in different statistical tests.
- What is statistical significance?
-
Statistical significance is a term used by researchers to land that it is unlikely their observations could accept occurred under the zip hypothesis of a statistical examination. Significance is ordinarily denoted by a p-value, or probability value.
Statistical significance is arbitrary – it depends on the threshold, or blastoff value, chosen 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 nix hypothesis.
When the p-value falls below the chosen alpha value, then nosotros say the result of the test is statistically meaning.
- What is the difference between quantitative and categorical variables?
-
Quantitative variables are any variables where the data represent amounts (eastward.1000. superlative, weight, or historic period).
Categorical variables are any variables where the information represent groups. This includes rankings (e.g. finishing places in a race), classifications (east.m. brands of cereal), and binary outcomes (e.chiliad. coin flips).
Yous need to know what type of variables yous are working with to choose the right statistical test for your data and translate your results.
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