Choosing which statistical test to use

Easy assessment to know which statistical test to use

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• Data
• Sample
• Purpose
• Method

Data

Choosing which statistical test to use

What type of data do you have?*

Categorical (often called rates)

• Mortality Rates (death/survival)
• Patient Falls Rates (fall/not fall)
• Compliance with Discharge Instructions (yes/no)

Quantitative

• Measurements
  • Temperatures
  • Blood Pressures
  • Pain Scale 1 to 10
• Counts
  • Number of Complications
  • Number of Hospital Visits
• Pre-established Scales

Nominal

Interval / Ratio

Sample

How many samples do you have?*

One Sample

Two samples

One sample, two measurements

Purpose

What is the test supposed to do?*

Testing against a value

Comparing two statistics

Looking for relationship

Method

Test for proportion

Let us consider the parameter p of population proportion. For instance, we might want to know the proportion of males within a total population of adults when we conduct a survey. A test of proportion will assess whether or not a sample from a population represents the true proportion from the entire population.

Critical Value Approach

The steps to perform a test of proportion using the critical value approval are as follows:

1. State the null hypothesis H0 and the alternative hypothesis HA.
2. Calculate the test statistic: 
   z=p^−p0p0(1−p0)n

   where is the null hypothesized proportion i.e., when 

3. H0:p=p0

4. Determine the critical region.

5. Make a decision. Determine if the test statistic falls in the critical region. If it does, reject the null hypothesis. If it does not, do not reject the null hypothesis.

 value Approach

Next, let’s state the procedure in terms of performing a proportion test using the p-value approach. The basic procedure is:

1. State the null hypothesis H0 and the alternative hypothesis HA.
2. Set the level of significance α.
3. Calculate the test statistic: 
   z=p^−pop0(1−p0)n

4. Calculate the p-value.

5. Make a decision. Check whether to reject the null hypothesis by comparing p-value to α. If the p-value <   then reject  ; otherwise do not reject  .

Difference of 2 proportions

Chi-Sqr for independence

Chi-square test( χ2 test)- chi-square test is used to compare two categorical variables. Calculating the Chi-Square statistic value and comparing it against a critical value from the Chi-Square distribution allows to assess whether the observed frequency are significantly different from the expected frequency.

The hypothesis being tested for chi-square is-

Ho: Variable x and Variable y are independent

Ha: Variable x and Variable y are not independent.

where o=observed , e=expected.

Regression analysis

Difference of 2 means (independence sample)

Test for a mean

Difference of 2 means (paired)

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• Data
• Sample
• Purpose
• Method

Data

Choosing which statistical test to use

What type of data do you have?*

Categorical (often called rates)

• Mortality Rates (death/survival)
• Patient Falls Rates (fall/not fall)
• Compliance with Discharge Instructions (yes/no)

Quantitative

• Measurements
  • Temperatures
  • Blood Pressures
  • Pain Scale 1 to 10
• Counts
  • Number of Complications
  • Number of Hospital Visits
• Pre-established Scales

Nominal

Interval / Ratio

Sample

How many samples do you have?*

One Sample

Two samples

One sample, two measurements

Purpose

What is the test supposed to do?*

Testing against a value

Comparing two statistics

Looking for relationship

Method

Test for proportion

Let us consider the parameter p of population proportion. For instance, we might want to know the proportion of males within a total population of adults when we conduct a survey. A test of proportion will assess whether or not a sample from a population represents the true proportion from the entire population.

Critical Value Approach

The steps to perform a test of proportion using the critical value approval are as follows:

1. State the null hypothesis H0 and the alternative hypothesis HA.
2. Calculate the test statistic: 
   z=p^−p0p0(1−p0)n

   where is the null hypothesized proportion i.e., when 

3. H0:p=p0

4. Determine the critical region.

5. Make a decision. Determine if the test statistic falls in the critical region. If it does, reject the null hypothesis. If it does not, do not reject the null hypothesis.

 value Approach

Next, let’s state the procedure in terms of performing a proportion test using the p-value approach. The basic procedure is:

1. State the null hypothesis H0 and the alternative hypothesis HA.
2. Set the level of significance α.
3. Calculate the test statistic: 
   z=p^−pop0(1−p0)n

4. Calculate the p-value.

5. Make a decision. Check whether to reject the null hypothesis by comparing p-value to α. If the p-value <   then reject  ; otherwise do not reject  .

Difference of 2 proportions

Chi-Sqr for independence

Chi-square test( χ2 test)- chi-square test is used to compare two categorical variables. Calculating the Chi-Square statistic value and comparing it against a critical value from the Chi-Square distribution allows to assess whether the observed frequency are significantly different from the expected frequency.

The hypothesis being tested for chi-square is-

Ho: Variable x and Variable y are independent

Ha: Variable x and Variable y are not independent.

where o=observed , e=expected.

Regression analysis

Difference of 2 means (independence sample)

Test for a mean

Difference of 2 means (paired)

Previous Submit Next

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We have received your answers.

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What does a statistical test do?

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p-value (probability value). The p-value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

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 extreme than the one calculated from the null hypothesis, then you 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 have 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 data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

1. Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
2. Homogeneity of variance: the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
3. Normality of data: the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data.

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test, which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be 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 test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (a.k.a ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (a.k.a integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal: represent data with an order (e.g. rankings).
• Nominal: represent group names (e.g. brands or species names).
• Binary: represent data with a yes/no or 1/0 outcome (e.g. 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 independent and dependent variables). Consult the tables below to see which test best matches your variables.

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 most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests are used to test cause-and-effect relationships. They look for the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means. They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g. the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g. the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether two variables are related without assuming cause-and-effect relationships.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Choosing a nonparametric test

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

Flowchart: choosing a statistical test

This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.