How do you summarise categorical data?
- frequencies, proportions or percentages
What test is used to compare the distribution of categorical variable to the hypothesised distribution?
chi squared goodness-of-fit test /one sample chi squared test
What is an example of a one-sample chi squared test hypothesis?
H0: is evenly distributed
H1: is not evenly distributed
Why is the one sample chi-squared test (chi squared goodness-of-fit test) used?
- to quantify the discrepancy between the expected and observed frequencies
e. g. between sample and hypothesised value
What is the shape of the chi-squared distribution?
- non-symmetric (always positive)
- changes with the df (degrees of freedom)
What is degree of freedom?
= number of groups -1
- indicates how many of the data points are ‘flexible’
What test is used to look at association between 2 categorical variables?
- chi-squared test of independence
How is the test statistic calculated for chi-squared test of independence?
- same as normal except need to calculate for each cell in the table
e. g. (column total x row total)/overall total
How do you calculate the df for a contingency table/cross-table?
df = (number of rows - 1) x (number of columns - 1)
What does a small x^2 value mean?
- when the observed value is approximately eyqla o the expected value in each cell
- only vary due to sample variability
What causes a large x^2 value?
- sample variability (given by p-value)
- Null hypothesis is not true
What are the chi-squared test of independence assumptions?
- the observational units are independent
- the expected cell counts should be >5
What are the limitations of x^2 test of independence?
- not informative about how variables are related
- only really be used for bivariate analysis
What are other options for assessing associations in categorical variables?
- relative risk
- odds ratio
Can chi-squared test of independence be used for before and after?
- no because the measurement is on the same individual
What is a McNemar’s test?
- used for 2x2 tables to test repeated measurments on the same variable
SIMPLE CONCEPT:
- if no change, participants stay on diagnoal
- if change, participants move off the diagonal
What test is used for continuous data?
one sample t-test
What is a t-test?
- parametric test used for testing differences in means
- tests the hypothesis that the means of a sample is equal to a fixed value
What does the one sample t-test assume?
- data is normal distributed
What is the test statistic equation for a one-sample t-test?
t = (sample mean - expected value)/ (sample sd/ square root of the sample size)
what influence the fatness of the t-test distribution tail?
- degrees of freedom
What makes a t-distribution more normally distributed?
- bigger sample size/more df
What is the t-test distribution if n>30?
- sampling distribution of means is approximately normally distributed
When is a two sample/independent sample t-test used?
compare two groups
- dependent is continuous
- independent is categorical
