7: T-test Flashcards
T-test
significant difference between the means of two groups. It helps you check if the difference you see is likely due to chance or a real effect.
The data-generating process is assumed to follow a normal distribution, given the group.
It assumes there is no difference (H0) p-value under 0,5 rejects this
it is the means/standard error
Types of T-test
o One-sample T-test: Compares the mean of a single group to a known value (e.g., average height of students vs. national average).
o Two-sample (independent) T-test: Compares the means of two independent groups (e.g., average scores of two different classes).
o Paired T-test (two-sample but not independent) : Compares means from the same group at two different times (e.g., before and after treatment).
o Non parametric alternative: when normality of the data can not be assumed (poisson, binomial or exponential)
Non parametric alternative: Wilcoxon test
Chi-Squared Test
used to determine whether there is a significant association between two categorical variables or to test how well an observed frequency distribution fits an expected frequency distribution (counts)
Pearsons chi(X^2) test and the larger X^2 the greater the difference between observed and expected frequencies
assumption counts need to be higher then 5
A small p-value (typically <0.05) indicates that the observed differences are statistically significant, leading to the rejection of the null hypothesis.
Multiple Testing
with multiple tests each can result in a false positive and increases the chances for false positives or type 1 errors -> Bonferroni correction (small studies) or FDR (large studies)
Calculating the chance in % of atleast 1 false positive
Bonferroni correction. FamilyWiseErrorRate. Type 1 errors (false-positive). the probability of rejecting at least one of the null hypothesis when all of them are true. FWER=1−(1−α)^k. K= number of individual statistical tests
state that the study found significant differences when there was none
To reduce Type I errors, you can lower the significance level, increase the sample size, and use methods to adjust for multiple comparisons.
Increased sample sizes can provide more accurate results, but they should be used carefully to avoid inflating the Type I error rate.
Types of errors
Type I error (false positive): rejecting the null hypothesis saying there is a difference when in fact there is not
Type II error (false negative): accepting the null hypothesis saying there is no differense when there is
Decreasing α: decreasing the significance level makes it harder to reject the null hypothesis. Effect: This reduces the risk of Type I errors but increases the risk of Type II errors (makes it harder to find positive results, which can lead to missing some true effects).
Increase sample size: Type I unchanged as reliable on α, type II down (When the effect size is large, it is easier to detect the effect)
Power
is the probability that a statistical test will correctly reject a null hypothesis that is false. In other words, it is the likelihood that the test will detect an effect when there is one present
