Comparing two means

Question 1

Give three reasons median splits are or are not effective in analysing data

Answer 1

Researchers should not compare artificially created groups in an experiment (e.g. based on the

median) .
1. Median splits change the original information drastically
2. Effect sizes get smaller
3. There is an increased chance of finding spurious effects

Question 2

In an equation with a categorical predictor with two predictors, what does b1 and b0 mean?

Answer 2

b1= difference between two group means 
b0= mean of the group coded as 0

Question 3

How is the t statistic related to the difference between two means?

Answer 3

Comparing the difference between the means of two groups is predicting an outcome based on membership of two groups. A t-statistic is used to ascertain whether a model parameter is equal to zero. In other words, the t-statistic tests whether the difference between group means is equal to zero.

Question 4

What two variants of the t test are there?

Answer 4

1. Independent t-test (independent measures t-test)
   This is comparing two means in which each group has its own set of participants.
2. Paired-samples t-test (dependent t-test)
   This is comparing two means in which each group uses the same participants.

Question 5

What assumption does the t test make?

Answer 5

That the null hypothesis is true

Question 6

Give the equation for the t test

Answer 6

𝑡 = 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑚𝑒𝑎𝑛𝑠 − 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒/𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 = (𝑋1 − 𝑋2) − 𝑋0/
𝑠𝑒

Question 7

What is the standard error of a sampling distribution known as?

Answer 7

standard error of differences.

Question 8

How does the standard error help the t test?

Answer 8

it gives a scale of how likely variability is between samples.

Question 9

What is meant by the variance sum law?

Answer 9

The variance sum law states that the variance of a difference between two independent variables is equal to the sum of their variances (e.g. the variance of x1-x2 = variance of x1 + variance x2).

Question 10

What does the variance sum law mean for the standard error?

Answer 10

The variance of the sampling distribution of difference between two sample means is equal to the sum of variances of the two populations from which the samples were taken.

Question 11

What equation is therefore used for se?

Answer 11

𝑠𝑒 = √ s21/ 𝑛1 + 𝑠22/𝑛2

Question 12

When is this equation only true? Otherwise what do we use?

Answer 12

This equation holds if the sample sizes are equal. If this is not the case, a pooled variance estimate is used instead.
s2p= (𝑛 −1)𝑠2 +(𝑛 −1)𝑠2 / 𝑛1 + 𝑛2 − 2

Question 13

How does this pooled variance look in a t test equation?

Answer 13

̅̅ 𝑡= 𝑋1−𝑋2/

√𝑠2𝑝/𝑛1+𝑠2𝑝 /𝑛2

Question 14

What assumptions does the paired-samples t test use?

Answer 14

assumption of normality to the sampling distribution of the differences between the scores.

Question 15

What three steps are involved in the procedure in a t-test

Answer 15

The data is explored (1), the t-test is conducted (2) and the effect size is calculated (3).

Question 16

What are levee’s tests used for ?

Answer 16

Tests whether variances are different in different in different groups

Question 17

What could. confidence interval containing 0 mean?

Answer 17

It is possible the two groups are the same as there is a possibility of the difference between the groups being 0

Question 18

What would a babes factor of .234 mean?

Answer 18

that the data is 0.234 times more likely to fall under the null hypothesis than the alternate hypothesis

Question 19

What formula is used to turn a t-value into an r-value?

Answer 19

𝑟=√ 𝑡^2/

𝑡^2 + 𝑑𝑓

Question 20

What does an r-value represent?

Answer 20

Effect size

Question 21

Describe what a bayesian factor means and how it can be used inversely

Answer 21

A Bayesian factor can be 0.005. This means that the data are 0.005 times as probable under the null hypothesis as under the alternative hypothesis. If you turn this around (by dividing 1/0.005), then you get 200. This means that the data are 200 times as probable under the alternative hypothesis as under the null hypothesis.

Question 22

What effect does using a t from a paired-samples test have on the effect size?

Answer 22

Using a t from a paired-samples t-test leads to an overestimation of the population effect size.

Question 23

Does this effect occur in an independent t test?

Answer 23

This does not occur when using an independent sample t-test.

Question 24

What can be used to combat the effect of a paired t test on effect size?

Answer 24

Cohen’s d