Chi square, significance testing & effect sizes

null hypothesis

assumes that any kind of difference between the chosen characteristics that you see in your set of data is due to chance

alternative hypothesis

states there is a statistically significant relationship between two variables. what we side with when out p values are small

null hypothesis significance testing

a method of statistical inference that compares an experimental factor to a hypothesis of no effect based on an observation

p-values

the probability under the assumption of no effect (null hypothesis) of obtaining a result equal to or more extreme than was actually observed.

what does a p-value have to be below for your result to be statistically significant

0.05

directional (one-tailed) hypothesis

predicts the direction of a relationship or difference between two variables

non-directional (two-tailed) hypothesis

states that there is a relationship between two variables without specifying the direction of that relationship

effect sizes

tells us the magnitude of difference/ similarity/ correlation

what does a Chi-squared test tell you and what is its purpose

used to compare observed results with expected results. Its purpose is the determine if this difference is due to chance or if there is a relationship between them

when is a Chi-squared test used

in nominal or ordinal variables

observed frequencies

number of times an event occurs in a real-world experiment

expected frequencies

number of times an event is expected to occur based on the probability or theory

what are the chi-squared test assumptions

• All frequencies must be unique/independent (so cannot be used for repeated measures/within subject designs)

• All expected values should be above 5 (if lots of conditions should be 1 or above)

• sample size is important

what test statistic do we report for the Chi-squared

and also degrees of freedom which is (r-1) (c-1)

How to report a Chi-squared test result

X² (degrees of freedom, N = sample size) = chi-square statistic value, p = p value.