Statistical tests Flashcards
What is the purpose of parametric tests?
Test for differences.
Test hypotheses.
Can be one or two-tailed tests.
What are the assumptions of parametric tests?
Continuous data.
Follows a normal distribution.
Variances (standard deviations) are homogenous.
Welch’s t-test can deal with unequal variances.
What is assumptions for parametric tests don’t hold?
The statistical test is in doubt and the p-value may be wrong.
You may be able to assume normality based on the type of data.
Robust test can withstand some deviation.
Can try to transform the data, or use a non-parametric test instead.
What are the types of parametric tests?
One-sample t-test
Paired t-test
Two-sample t-test
What is a one-sample t-test?
Used to determine if the mean of a sample Is different from an expected value.
What is a paired t-test?
Test for differences between two sets of paired observations.
e.g. before vs after treatment.
What is the null hypothesis of the paired t-test?
The mean difference (or change) is zero.
What is the rationale of the paired t-test?
Calculate the difference between each pair of points, then determine if the mean of these values is different from 0.
What is the method of the paired t-test?
Calculate the difference between each pair of measurements.
Calculate the mean difference and standard error.
Calculate the p-value and compare to pre-selected significance level.
What is a two-sample t-test?
Test whether the means of two independent sets of measurements are different.
What are the assumptions of the two-sample t-test?
Samples are independent of each other.
Also need to check that appropriate t-test assumptions are met.
What is the null hypothesis for two-sample t-tests?
The difference between the two means is zero.
i.e. the two samples come from populations with the same mean value.
What is a one-sample t-test?
Used to determine if the mean of a sample Is different from an expected value
What is the null hypothesis for one-sample t-tests?
There is no difference between the population mean and the given value.
Alternative hypothesis: the population mean is different from the given value.
What are types of parametric tests?
Assume that the data follow some predetermined pattern, or parameters, such as they are collected from a normally distributed population.
t-tests and ANOVA are parametric tests.
What are non-parametric tests?
Non-parametric equivalents do not assume anything about where the data came from.
e.g. Mann-Whitney U test.
What are the advantages of non-parametric tests?
Allows hypothesis testing where structure of population sampled is unknown.
Can analyse data that consist of ranks (ordinal scale data) or classifications (nominal scale data).
What are the disadvantages of non-parametric tests?
Wastes data if you could apply a parametric method instead.
Less sensitive, so important effects can be missed.
What is the Wilcoxon test?
Non-parametric Equivalent of paired T-test
If the sampled values are not from a normal distribution, the Wilcoxon test can be used.
Procedure involves calculating differences, as for the paired T rests.
Uses ranks of the differences.
What is the Mann-Whitney U test?
Non-parametric unpaired T-test equivalent.
Ranks of measurements used, not the measurements themselves.
Very powerful non-parametric test.
Can perform one or two tailed tests.
What is the one sample sign test?
Non-parametric one sample t-test equivalent.
Uses ranks and not measured values.
Compares against expected values.
This is a type of Wilcoxon paired test where one of the two samples is replaced by the expected value.
What are the problems with using multiple t-tests?
Very time consuming - if 4 groups, then 6 tests.
Multiple testing increases our chance of type I errors - falsely rejecting the null hypothesis.
What is ANOVA?
Analysis of variance.
Used to determine differences between multiple groups.
Looks at variability of the data rather than directly at the means.
What are the assumptions of ANOVA?
Continuous data in each group.
Variance homogeneity in each group.
Samples are independent.
What happens if the assumptions of ANOVA don’t hold?
The p-value may be inaccurate.
Try data transformation.
Use a non-parametric equivalent test.
What is one-way ANOVA?
Compares the mean from multiple independent samples
Gives an overall p-value.
What is the null hypothesis for one-way ANOVA?
The samples for each group come from populations with the same mean values.
What is the alternative hypothesis for one-way ANOVA?
One or more of the groups are different from one or more of the others.
If variability if far enough then assumes the groups are different.
If they are different, then can use post hoc tests to determine which groups are different.
How does one-way ANOVA work?
It separates total variability in the data into:
Between-group variance - differences between individuals from the different groups.
Within-group variance - differences between individuals within each group.
What are the results of the one-way ANOVA?
If there are differences between groups, the between-group variance will be larger than the within-group variance.
Test is based on the ratio of the between-group and within-group variances.
How are the variabilities in one-way ANOVA calculated?
The between-group variability is the sum of squares of the distance from each point’s group mean to the overall mean.
The within-group variability is the sum of squares of the distances from each point to its group mean.
What are repeated measures ANOVA?
Tests whether the means of two or more groups of related measurements are different.
What is two-way ANOVA?
Tests the effect of two factors at once.
e.g. test the effects of two treatments.
What are Post-Hoc tests?
If the ANOVA gives a statistically significant result, further tests can be done to determine which groups are different.
What is the Kruskal-Wallis test?
Non-parametric extension of the Mann-Whitney U test.
Null hypothesis - there are no differences in the distributions of groups.
The sums of the ranks in each of the groups should be comparable.
