Unit 3 T-tests & Non-Parametric solutions

Question 1

How can we test differences in the mean

Answer 1

One (single) sample t-test
Independent samples t-test
Paired sample t-test

Question 2

A one (single) sample t-test is for:

Answer 2

assessing if the sample (one sample) mean differs significantly from a particular (theoretical) value

Question 3

An Independent samples t-test is for:

Answer 3

When we have two means, two groups, independent, no relation between each, e.g. randomly assigned to
each group

Question 4

A Paired sample t-test is for:

Answer 4

dependent (related samples), e.g. before and
after experiments on the sample plot or same individual

Question 5

Whats a one-tailed directional hypothesis

Answer 5

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

Question 6

Whats a Two tailed non-directional hypothesis

Answer 6

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.

Question 7

What’s the difference between the left & right tail in a one-tailed hypothesis

Answer 7

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.

Question 8

What are the tails in a two-tailed hypothesis telling you

Answer 8

Testing for the possibility of the relationship in both directions. Testing a new drug less effective or more effective than an existing drug?

Question 9

What is Cohen’s Effect size - one sample t-test

Answer 9

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.

Question 10

Formula for Cohen’s d effect size =

Answer 10

Mean difference(Mean of group 1 - Mean of group 2) / Standard Deviation

Question 11

What test do you use when comparing two populations means?

Answer 11

two samples t-tests and
paired samples t-test

Question 12

What test do you use when comparing two populations variances?

Answer 12

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)

Question 13

What is Confidence Interval

Answer 13

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.

Question 14

What is the Effect size for independent t-test

Answer 14

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.

Question 15

Whats Fishers F-test (variance ratio test) for

Answer 15

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)

Question 16

Fishers F-test is restricted to…

Answer 16

comparison of two variances/groups.
Assumes a normal distribution.

Question 17

Whats a Levene’s t-test

Answer 17

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.

Question 18

What does p-value tell us in Levene’s t-test

Answer 18

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.

Question 19

Whats a paired sample t-test for

Answer 19

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

Question 20

What does a paired sample t-test assume

Answer 20

Assumes that the differences between pairs are normally distributed.
Does not assume the samples have equal variance.

Question 21

Whats a Mann Whitney U test for

Answer 21

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.

Question 22

Whats a Wilcoxon matched pairs tests

Answer 22

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.