Lecture 6 Flashcards
Tests of Significance (I)
What are the two main groups of statistical test?
Parametric and Non-Parametric
Parametric Test Use
May used when population is normally distributed
Nonparametric Test Use
Must be used when population isn’t normally distributed/ no assumption can be made about population distribution
Parametric Tests Compare…?
Means and Variances
Tests to see if data is normally distributed
Shapiro-Wilk and Kolmogorov Smirnov (K-S/KS)
Which type of test is more powerful?
Parametric
Parametric Test Examples
T-Tests and AVOVA
What do T-Tests Compare?
Always used to make comparisons between 2 sample means (or one sample mean and one known population mean)
What does ANOVA Compare?
Used when 2+ samples come from the same population. The variation within each sample is compared to the variance between sample means
T-Test
Student’s t-test. Used to compare normally distributed data with similar standard deviations. Typically used to compare one or two samples. Test the probability that the samples come from a single population with single mean. Work well with smaller samples (n ~ 30)
Two Tailed T-Tests
When null hypothesis is allowed to be rejected from either direction (high or low)
One Tailed T-Tests
We reject the null hypothesis only when the result is in a single tail of the test distribution
When do we reject a null hypothesis?
We reject because the mean value of one sample is higher than that of the other sample - or it is lower
3 Types of T-Test
One sample t-test, Paired samples t-test (AKA paired t-test, related t-test) and Independent Samples t-test (AKA Unpaired t-test, Two-samples t-test)
One Sample T-Test
Investigate whether there’s a difference between a group and a standard value or whether a subgroup belongs to a population
Paired-Samples T-Test
Investigate whether there’s a difference within a group between two points in time or under different conditions (within-subjects)
Independent-Samples T-Test
Investigate whether there’s a difference between the same variable in two different groups (between-subjects)
Why ANOVA over T-Test?
Single test covers all comparisons (rather than a t-test for every individual comparison). Can also consider the effects of multiple factors on a variable of interest
Limitations of T-Tests
Threshold for significance is P = 0.05. There is still a 5% chance that we have come to wrong conclusion. If we perform multiple t-tests then this 5% chance is repeated each time
Why shouldn’t we do multiple T-Tests?
The more t-tests we do for the same comparison, the greater the chance of coming to the wrong conclusion
What does an ANOVA do?
ANOVA tests compare the variability between samples with the variability within samples
Types of ANOVA
One-way ANOVA and Repeated-Measures ANOVA
One-Way ANOVA
Used when we want to compare means from more than two samples. We can consider this type of ANOVA as simply an extension of the t-test. 1 factor and 1 result. (E.g. effect of studying techniques on exam scores)
Repeated-Measures ANOVA
Is used when there are repeated measurements on the same sampling unit. 2 factors and 1 result. (E.g. effects of diet + exercise for weight loss)
Post hoc test
Compares all samples against one another and report a p-value for each comparison
