Inferential Statistics
Sample Types in Analyses
When comparing groups, samples might be: Independent: two different groups are compared (ex. treatment and comparison groups). Paired: two measures in one group are analyzed (ex. before and after experiment).
Parametric
Used for discrete and continuous variables Relies on probability distribution assumptions Relies on assumptions about population Normal distribution is sought for
Tests of Difference
Chi-square: used to determine whether a difference between 2 categorical variables in a sample is likely to reflect a real difference between these 2 variables in the population McNemar: applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal ("marginal homogeneity") Mann-Whitney: assessing whether one of two samples of independent observations tends to have larger values than the other Wilcoxon: used when comparing two related samples or repeated measurements on a single sample to assess whether their population mean ranks differ Kruskal-Wallis: testing whether samples originate from the same distribution. It is used for comparing more than two samples that are independent, or not related Friedman: used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns Independent T test: tests whether it is likely that the samples are from populations having different mean values Paired T test: used to compare the values of means from two related samples, for example in a 'before and after' scenario One-Way ANOVA: provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t-test to more than two groups (independent) Repeated Measures ANOVA: provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t-test to more than two groups (paired)
Hypothesis testing
Done in two ways: Analysis of Difference: analysis of difference between two or more samples/groups in terms of specific variables. Ex: H0: Section A and Section D students are not different in terms of their grades H1: Section A and Section D students are different in terms of their grades Analysis of Association: analysis of relationships between variables in a sample. Ex: H0: There is no relationship between attendance and grades H1: There is a relationship between attendance and grades
Two Types of Tests
Parametric and Non-Parametric
Inferential Statistics
We use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data. It is about inferences about population based on the findings about sample. It involves predicton and hypothesis testing.
Estimation
Two types of estimation: Point Estimation: the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" or "best estimate" of an unknown (fixed or random) population parameter Interval Estimation: the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter
Non-Parametric
Used for nominal and ordinal variables Does not rely on probability distribution assumptions Does not rely on assumptions about population Normal distribution is not sought for
Two ways to infer from statistics
Estimation = estimating about the population parameters based on the statistics from the randomly selected sample. Hypothesis Testing: finding out if there is any relationship between variables of the randomly selected sample in order to decide about the population.
