GOF Tests
What is the purpose of a chi-squared goodness of fit test?
To determine whether an observed distribution fits an expected distribution.
What is the difference between homogeneity and independence tests?
Homogeneity compares distributions across multiple populations; independence checks the association between 2 variables in one population.
What does the slope represent in a linear regression model?
The change in the response variable for each one-unit increase in the explanatory variable.
What test is used to compare one sample mean to a known value?
One-sample t-test.
What symbol represents a population proportion?
p
One categorical variable.
How many categoricak variables are used in a chi-squared test of independence?
2 categorical variables
What is the null hypothesis in a linear regression significance test?
B=0
What distribution is used for mean tests when the population standard deviation is unknown?
t-distribution
When should you use a one-proportion z-test?
When comparing one sample proportion to a claimed population proportion.
What is the formula to calculate the chi-squared test statistic?
(Observed- expected)^2 / expected
The 2 variables are independent (no association)
What condition checks for a linear relationship between variables?
The relationship should be approximately linear.
What condition checks the shape of the population for small samples?
The population should be approximately normal.
What condition checks randomness in proportion tests?
The data must come from a random sample or randomized experiment.
What condition must be met for expected counts in a chi-squared test?
All expected counts should be at least 5.
How do you calculate an expected count in a 2 way table?
(Row Total * Column Total)/ Grand Total
What does r^2 represent?
The proportion of variability in the response variable explained by the model.
What is the null hypothesis for a two-sample t-test?
M1=M2
What is the null hypothesis for a two-proportion test?
p1=p2
In context, what does rejecting the null hypothesis mean for a goodness-of-fit test?
There is convincing evidence that the distribution differs from what was expected.
If the p-value is very small, what conclusion should be made?
Reject the null hypothesis; There is evidence of an association/no difference between the variables.
Why is it important to check residual plots?
To verify conditions such as linearity, constant variance, and independence.
What does a confidence interval for a mean difference that includes 0 imply?
There is no statistically significant difference between the 2 means.
Why do we combine proportions in a two-proportion z-test?
Because the null hypothesis assumes the two population proportions are equal.