E-module 2 - choosing more statistics

Question 1

What are the tests for correlation/similarity?

Answer 1

Discrete data - Chi-squared test
Continuous, normally distributed - Pearson’s Correlation test
Continuous, not normally distributed - Spearman’s Rank Correlation test

Question 2

What are the parametric tests for difference?

Answer 2

Unpaired t-test - used to compare the SAME variable between two DIFFERENT groups
Paired t-test - used to compare DIFFERENT variables within the SAME group

One-way ANOVA - comparing a variable between 3 or more groups with a normal distribution

Question 3

What does the ANOVA test require after use and why is this?

Answer 3

Requires a post-hoc test (Tukey p-h test or Bonferonni p-h test) (p-h = post hoc)
- this is because, while the ANOVA will show you if the means are different between A, B, and C, it doesn’t show you where the differences lie i.e. between AB, AC, BC etc - this requires the post hoc

Question 4

What are the non-parametric tests for difference?

Answer 4

Wilcoxon signed rank test - 2 groups, paired, not normally distributed
Mann-Whitney U test - 2 groups, unpaired, not normally distributed
Kruskal-Willis test - 3 or more groups, paired, not normally distributed
Friedman test - 3 or more groups, unpaired, not normally distributed

Question 5

What is regression?

Answer 5

Regression QUANTIFIES the association between two variables, which has been identified, or not, by correlation tests.
- regression tells us the impact of changing one variable on the other variable

Question 6

What is the mathematical basis for regression and how does it work?

Answer 6

Regression can be defined as the equation of a line, y = mx + c

• m is the gradient of the line, aka the regression coefficient
• c is the y-axis intercept value

This works as if you use this equation, you can calculate the corresponding x value f you have the y value and vice versa

Question 7

What is the relationship between regression and correlation?

Answer 7

Correlation indicates the strength of the relationship between two variables.
Regression then quantifies that association
- so after correlation testing, you could establish a line of regression using the regression coefficient in order to estimate values of each variable based on a starting value of the other variable

Question 8

When should you use a chi-squared test?

Answer 8

When you have counted quantitative data and you want to see if there is an association/difference between your data sets.
- IMPORTANTLY, this test only tells you if a difference exists, it does not tell you the magnitude of the difference

Question 9

What is the set up for a chi-squared test?

Answer 9

You have your observed values
You need to produce your expected values (based on your null hypothesis)
Then plot them in a 2x2 table with totals along each axis
You get a chi-squared statistic which you then compare with tables that give you a p-value for your given chi-squared value
You can then compare your p-value to your significance level
Finally, draw your conclusion based on the significance of your p-value.