Public Health: Tests

• Nominal
  • Sex, blood, type, color, dog breed, affiliations...
• Ordinal
  • Class range, age group, educational level, income level..

Categorical data are basically word or label answers.

Summary data is usually stated as frequencies, proportions, rates, or percentages.

EX: Do you have siblings? Yes/No

Don’t be trick because you count the number of yes and no responses for example. You count to get a proportion that said yes and the proportion that said no. The data itself is not a count.

• Chi Square
  • A chi-square test is used when you want to see if there is a relationship between two categorical variables.
• Fisher's Exact Test
  • The Fisher’s exact test is used when you want to conduct a chi-square test but one or more of your cells has an expected frequency of five or less. 
• McNemar
  • Use if you were interested in the marginal frequencies of two binary outcomes. 
• Mann-Whitney
  • Is the  non-parametric alternative test to the independent sample t-test.
  • Used to compare two sample means that come from the same population.
  • Used when the data is ordinal or when the assumptions of the t-test are not met.
• Kruskal-Wallis
  • Used when you have one independent variable with two or more levels and an ordinal dependent variable. 
  • It is the non-parametric version of ANOVA.
• Spearman's Rank Correlation
  • Used to test the association between two ranked variables, or one ranked variable and one measurement variable.
• Wilcoxon Rank sum Test
  • Used when you don't assume that the difference between the two variables is interval and normally distributed but you do assume the difference is ordinal. 
  • Non-parametric version of a paired samples t-test

• Interval
  • IQ score, temperature...
• Ratio
  • Weight, height, pulse rate...

Continuous Data are also called quantitative date and are expressed in numbers.

Examples include temperature, blood pressure, pain scale. Counts are also included such as number of hospital stays or number of adverse events. 

Summary data is expressed as a mean. 

EX: How many siblings do you have?

• Single sample t-test
  • Compares a sample mean to a known population mean.
  • EX: Comparing ACOM students' average MCAT scores to the national average MCAT score.
• Independent samples t-test (unpaired)
  • Compares two distinct samples.
  • EX: Comparing ACOM students' average MCAT score to the average of another school.
• Dependent samples t-test (paired)
  • EX: Comparing the average test score before pet therapy and then after pet therapy. 
  • Other examples: before and after treatment of a patient or comparing twins.

t-tests vs. z-test

In general, use the t-test if you DO NOT know what the standard deviation is and z-test when you do know the standard deviation. In general, this mean t-tests is used for small samples and the z-test for large ones. 

You use ANOVA (analysis of variance) when there are three or more samples you want to analyze at once. 

Two types of ANOVA:

1. One Way ANOVA
   • Compares three or more unmatched groups.
2. Two Way ANOVA
   • Determines how a response is affected by two factors.

Correlation answers questions about strength and direction of the correlation, association, relationship, etc between two variables. 

For those of you that want to know more the Math & Science people have created a nice set of short videos on a variety of statistics topics.