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.
