Unit 3 T-tests & Non-Parametric solutions Flashcards
How can we test differences in the mean
One (single) sample t-test
Independent samples t-test
Paired sample t-test
A one (single) sample t-test is for:
assessing if the sample (one sample) mean differs significantly from a particular (theoretical) value
An Independent samples t-test is for:
When we have two means, two groups, independent, no relation between each, e.g. randomly assigned to
each group
A Paired sample t-test is for:
dependent (related samples), e.g. before and
after experiments on the sample plot or same individual
Whats a one-tailed directional hypothesis
predicts the nature of the effect of the independent variable on the dependent variable.
For example, we are only interested in pollutant
levels being significantly larger than a maximum threshold marked by legislation
Whats a Two tailed non-directional hypothesis
Predicts that the independent variable will have an effect on the dependent variable, but the direction of the effect is not specified.
E.g.,
differences in temperature are significantly different either above or below certain reference value.
What’s the difference between the left & right tail in a one-tailed hypothesis
Left tail looks at areas where there is a reduction. Eg. in the no. of species/individuals or a negative effect.
Right tail looks at areas where theres an increase. Eg. in the no. of species, or a positive effect.
What are the tails in a two-tailed hypothesis telling you
Testing for the possibility of the relationship in both directions. Testing a new drug less effective or more effective than an existing drug?
What is Cohen’s Effect size - one sample t-test
Effect size is a quantitative measure of the magnitude of the experiment effect.
The larger the effect size the stronger the relationship between the two variables.
Cohen’s d is an appropriate effect size for the comparison between two means.
Formula for Cohen’s d effect size =
Mean difference(Mean of group 1 - Mean of group 2) / Standard Deviation
What test do you use when comparing two populations means?
two samples t-tests and
paired samples t-test
What test do you use when comparing two populations variances?
Variance ratio test or
Fisher’s test and Levene’s test.
Comparing two variances is needed before embarking on a parametric comparison of the means: normal distribution and equal variance conditions need to be met in t tests, anovas etc.
Fisher’s F-tests (normal) and Levene’s tests (non-normal)
What is Confidence Interval
Confidence intervals measure the degree of uncertainty or certainty in a sampling method.
Level of significance is a statistical term for how willing you are to be wrong. With a 95 percent confidence interval, you have a 5 percent chance of being wrong.
What is the Effect size for independent t-test
A quantitative measure of the magnitude of the experimenter effect.
The larger the effect size the stronger the relationship between two variables.
Cohen’s d is an appropriate effect size for the comparison between two means.
Whats Fishers F-test (variance ratio test) for
Used with normal distributions: not robust outside normality.
Test if variances of two populations (1 and 2) are equal (2-tailed) or one variance is larger than another (right, one-tailed test)
Fishers F-test is restricted to…
comparison of two variances/groups.
Assumes a normal distribution.
Whats a Levene’s t-test
An inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. Some common statistical procedures assume that variances of the populations from which different samples are drawn are equal.
Levene’s test assesses this assumption.
What does p-value tell us in Levene’s t-test
if p value is less than or equal to 0.05 assumption is wrong and variances are sig. diff. (equal variances are not assumed)
if p value is greater than 0.05 then equal variances are assumed.
Whats a paired sample t-test for
Used to measure change over time, or compare before/after.
Matched, paired, bivariate data: not independent.
Tests whether the mean difference in the pairs (before & after) is different from 0-H1
What does a paired sample t-test assume
Assumes that the differences between pairs are normally distributed.
Does not assume the samples have equal variance.
Whats a Mann Whitney U test for
Tests by comparing the rank of observations in 2 groups. Testing using one independent variable that consists of two categorical, independent groups.
Assumes data from independent random samples.
Data must be measured at least at the ordinal or continuous level.
Whats a Wilcoxon matched pairs tests
Signed ranks test for two related samples.
Test if medians of two paired measurements made on identifiable population are different from each other.
Non-parametric equivalent of the paired t-test.
