Differences, Frequencies and Relationships

Question 1

Why cant t-tests be used for testing between more than 2 groups?

Answer 1

Very time consuming as 4 groups would require 6 t-tests

Multiple testing increases our chance of making type 1 errors

Question 2

What is ANOVA?

Answer 2

Analysis of Variance

Question 3

When do we use ANOVA?

Answer 3

Used to determine differences between more than 2 groups

Question 4

What does ANOVA look at?

Answer 4

Looks at the variability of the data rather than directly at the means

Question 5

What are the assumptions of ANOVA?

Answer 5

Continuous data within each group
Equal variance in each group
Samples are independent
Need 3 or more groups to test

Question 6

What happens if the assumptions of the ANOVA are not held/met?

Answer 6

P value may be wrong

Question 7

What should you do if the assumptions of the ANOVA are not met?

Answer 7

Try transforming the data
Use a non-parametric equivalent test
If samples are not independent then need another method

Question 8

What does the one way ANOVA do?

Answer 8

Compares the means from 3 or more independent samples giving overall P values

Compares the test statistic to an F distribution

Question 9

What are the null hypothesis for a one way ANOVA?

Answer 9

The samples for each group come from populations with the same mean values.

Question 10

How does the one way ANOVA separate the variability?

Answer 10

Separates total variability in the data into:

Between group variance (treatment factor; differences between individuals from the different groups)

Within group variance (unexplained residual error; random variation between individuals within each group)

Question 11

For a one way ANOVA, what would it mean if there are differences between the groups?

Answer 11

Then the between group variance will be larger than the within group variance.

Question 12

How does the one way ANOVA work?

Answer 12

• Just use 2 groups for the illustration example – hypothetical weights for 2 groups of fish
• (a) Calculate the overall mean & the group means
• (b) The total variability is the sum of squares of the distances of each point from the overall mean; broken down into between-group variability & within-group variability
• (c) The between-group variability is the sum of squares of the distances from each point’s group mean to the overall mean
• (d) The within-group variability is the sum of squares of the distances from each point to its group mean

Question 13

What are some other ANOVA tests?

Answer 13

Repeated measures ANOVA

Two way ANOVA

Question 14

what is the purpose of the repeated measures ANOVA?

Answer 14

tests whether the means of two or more groups of related measurements are different

Question 15

what is the purpose of the two way ANOVA?

Answer 15

tests the effect of two factors at once (e.g. crop yield effect by adding different amounts of nitrate and phosphate)

Question 16

What is the Kruskal-wallis test?

Answer 16

Extension of the Wilcoxon rank sum test

Question 17

What is the Chi-square test used for?

Answer 17

It is used to discover if there is a relationship between categorical variable

Question 18

What are the assumptions of the Chi-square test?

Answer 18

Variables should be categorical (ordinal or nominal)
Should have two or more groups
All expected frequencies must be greater than 5

Question 19

What is the purpose of the Chi-square test?

Answer 19

Test whether characteristics are different from expected values

Measures difference between the observed and expected values.

Question 20

What is the null hypothesis of the Chi-square test?

Answer 20

the ratio obtained is equal to that expected

Question 21

How do you determine the significance probability of the chi-square test?

Answer 21

Compare the value of 𝜒2with the critical value of the 𝜒2 statistic for (N-1) df (N is the number of character states, e.g. 2-1), at the 5% significance level

Question 22

How do you decide to accept or reject the null hypothesis of the chi-square test?

Answer 22

If 𝜒2 ≥ critical value, reject the null hypothesis, concluding that the distribution is significantly different from expected

If 𝜒2 < critical value, the null hypothesis cannot be rejected, concluding that no significant difference from expected was found

Question 23

How can the chi-square test be used for associations?

Answer 23

• Tests whether the character frequencies of 2 or more groups are associated in some way
Looks to see if the characteristic is distributed randomly or not

• Determining the expected frequencies is the tricky part
• Uses the same methodology once the expected values have been determined

Question 24

What are the two main tests for relationships?

Answer 24

Linear regression

Correlation

Question 25

What is the first thing to do when we Want to know if and how two sets of measurements (continuous variables) are associate

Answer 25

Draw a scatter plot

Question 26

What is the outcome variable?

Answer 26

The dependent or response variable

Question 27

What is the predictor variable

Answer 27

The explanatory or independent variable

Question 28

How are the scatter plots for a relationship test composed?

Answer 28

Predictor variable on x axis and outcome on the y axis

Question 29

What is the purpose of the linear regression test?

Answer 29

quantify the linear relationship between two sets of paired measurements

Question 30

What are outliers?

Answer 30

Extreme values found in a data set that can skew the data and affect the mean.

Question 31

What is the purpose of the correlation test for relationships?

Answer 31

test to determine whether there is a linear association between two sets of paired measurements

Question 32

What are the assumptions of the correlation test?

Answer 32

At least one variable is Normally distributed

Linear relationship between variables

You can try to transform data to fulfil either of these requirements

Question 33

What test do you use if the correlation assumptions cannot be met?

Answer 33

Pearson’s Rank correlation

Question 34

What are the two types of Rank correlation test?

Answer 34

Spearmans

Kendalls

Question 35

When do we use spearmans rank correlation test?

Answer 35

If a significance test is required then use spearmans

Question 36

When do we use Kendalls rank test?

Answer 36

If there is an estimate of strength of correlation

Question 37

How do we tell between association and relationships?

Answer 37

Are two variables associated

Correlation tests for a linear relationship

Linear regression quantifies the relationship