Unit 4 - Inferential statistics

Why are statistical tests used?

To check whether results are mathematically sound.

What is statistical significance?

This refers to the likelihood (or probability) that results are due to chance. If your results are statistically significant, it suggests a difference (cause and effect) or that there is a correlation between co-variables.

What is probability?

This refers to the likelihood that results are due to a real difference/correlation you are testing.

What is a significance level?

A numerical value that tells you the margin of error that could occur in your results.

What is accepted as a probability value (p value) in psychology?

95%, meaning that results are due to chance in a maximum of 5% of cases. This converts to a significance level of 0.05.

What are the five statistical tests you must know?

• Sign test

• Chi square

• Wilcoxon matched pairs signed ranks test

• Mann Whitney U

• Spearman’s rank order correlation co-efficient 

What are observed or calculated values?

The numerical value that is created as a result of inferential statistical analysis of your data. This will be compared to critical values for the test to calculate the level of significance. Each test creates an observed value that is signified with a symbol or letter, before a numerical value.

What are critical values?

Numbers taken from pre-calculated tables for each test. The numerical values in the table have been assigned to a particular inferential statistical test by mathematicians and are used by all scientists. Critical values are compared to the observed value for your set of data. This allows researchers to determine whether they should accept or reject their experimental hypothesis depending on whether the critical value is higher or lower than the observed value (test dependent).

Sign test

Conditions of use: study of difference, nominal data, repeated measures

Observed value: S

The observed value (S) must be less than or equal to the critical value for results to be statistically significant

Chi square

Conditions of use: study of difference, nominal data, independent groups

Observed value: X²

The observed value (X²) must be greater than or equal to the critical value for results to be statistically significant

Wilcoxon matched pairs signed ranks test

Conditions for use: study of difference, at least ordinal data, matched pairs

Observed value: T

The observed value (T) must be less than or equal to the critical value for results to be statistically significant

Mann Whitney U

Conditions for use: study of difference, at least ordinal data, independent groups

Observed value: U

The observed value (U) must be less than or equal to the critical value for results to be statistically significant

Spearman’s rank order correlation co-efficient

Conditions for use: relationship (correlation), at least ordinal data

Observed value: Rho

The observed value (Rho) must be greater than or equal to the critical value for results to be statistically significant

How can you remember which tests require the critical value to be greater than the observed value to be statistically significant?

The ‘R up’ rule. If there is an R in the short name of the test, like Chi squaRe and SpeaRman’s Rank, then the observed value (X² or Rho) needs to be greater than or equal to the critical value for results to be considered statistically significant. If there is not an R in the short name of the test, like Sign, Wilcoxon or Mann Whitney, then the observed value (S, T, U) must be less than or equal to the critical value for results to be statistically significant.

Example statistical statements for Sign, Wilcoxon and Mann Whitney

As the observed value is less than or equal to the critical value (…), the results are statistically significant at 0.05 level. Therefore, we accept the experimental hypothesis and reject the null hypothesis.

As the observed value is greater than or equal to the critical value (…), the results are not significant at 0.05 level. Therefore, we reject the experimental hypothesis and accept the null hypothesis. 

Example statistical statements for Chi square and Spearman’s rank

As the observed value (X², Rho) is greater than or equal to the critical value (…), the results are statistically significant at 0.05 level. Therefore, we accept the experimental hypothesis and reject the null hypothesis.

As the observed value (X², Rho) is less than or equal to the critical value (…), the results are not significant at 0.05 level. Therefore, we reject the experimental hypothesis and accept the null hypothesis.