What does each statistic has?
its own comparison distribution
-> e.g.: Mean = Standard distribution
What does the comparison distribution allows us to?
-> allows us to know the probability of a statistic taking a certain value within a population
-> allows us to make inferences
What are the 2 steps of the inferential statistic process?
- To know the appropriate statistic (a Good parameter 𝜃 estimator).
- To know its comparison distribution.
What is hypothesis testing on means used for?
to compare a sample mean to a known (or hypothetical) population mean
How many samples does hypothesis testing require?
only one, no need to compare between groups
What are the Comparison distributions when the population variance / SD is known?
Standard (normal) distribution
What are the Comparison distributions when the population variance / SD is unknown?
Student’s T:
* Symmetric.
* From –Infinte to Infinite.
* Mathematical expectation (mean) = 0.
What do we use when we have two means?
the student’s t comparison distribution
What does independent mean in comparing two means?
- The samples belong to different groups of people
- requires a quantitative variable and a dichotomous categorical variable
-> assumption of homosecedasitcity: equal variances (levenes test)
What does dependent mean in comparing two means?
- Same group of participants, but measured at different times.
- Requires 2 related quantitative variables.
What do we have to check for between population means?
- differences between sample means
- differences between population means
What is the mean classified as when we have an unknown population variance?
as T score (observed)
-> then compared to expected or theoretical t (tables)
When do we use ANOVA (analysis of Variance)?
when we want to do a hypothesis testing on more than two means
When do we use the Pearson Chi-Square (x²)?
To infer/decide whether the same relationship is found in the population.
-> Two categorical variables.
-> It measures the difference between observed frequencies (f o ) and expected frequencies (f e ) in the contingency tables.
What is a decision rule in Pearson Chi-Square tests?
Decision rule: If the probability of X 2 (𝛘 2 of the sample), is lower than the critical value (𝛘 2 theoretical, table), Accept H0 . If it is greater, Reject it.
What is the possibly most applied test?
the Pearson correlation (p)
What can the Pearson correlation be?
parametric (normal distribution, quantitative variables) and linear (two-tailed test, left one-tailed test and right one-tailed test)
