Comparing Two Groups

Question 1

How do you compare two unrelated groups (apples and oranges)?

Answer 1

By comparing their z score (standard deviation)

Question 2

What test do you use to compare your data against a theoretically predicted mean?

Answer 2

One sample t-test

Question 3

In one-sample t-tests, what do these symbols mean?

Answer 3

X = The sample mean we actually observed

μ = true population mean if the null hypothesis is correct

Question 4

In one-sample t-tests, what does σ mean?

Answer 4

SEM (standard error of the mean)

Question 5

What is the R code for one-sample t-tests?

Answer 5

t.test(x, y)

x = the variable containing raw data

y = true population mean, according to null hypothesis

alternative: oneSampleTTest(x, y)

Question 6

What is the symbol for the test statistic in a one-sample t-test?

Answer 6

t

Question 7

Since one-sample t-tests are unsure about what the true standard deviation is, how do they obtain the overall sampling distribution for the t-statistic?

Answer 7

Average over lots of possible choices for the standard deviation.

Question 8

What happens to the sampling distribution of t as the sample size (N) grows larger?

Answer 8

Our estimate of the standard deviation is more precise and the t-distribution grows similar to normal.

Question 9

How are degrees of freedom calculated for a t-distribution?

Answer 9

N-1

N = number of data points

1 = number of constraints (i.e. the mean)

Question 10

How is the t-tests t statistic calculated

Answer 10

(Sample mean we observed - true population mean if the null hypothesis is correct)

/ (divided by)

(The true population standard deviation / SEM)

Question 11

Because the width of the t distribution depends on sample size, the size of the rejection region changes as ___ increases

Answer 11

N

(number of data points)

Question 12

What is Cohen’s d?

Answer 12

A simple measure of effect size

Question 13

How do you interpret Cohen’s d (roughly)

Answer 13

Question 14

How do you run Cohen’s d in R?

Answer 14

library(lsr)

>cohensD(x, y)

(x,y same as t-test)

Question 15

How do you write up the results of a one-sided t-test

Answer 15

e.g. (t(19) = 3.42, p = .003)

Question 16

How do you write the null hypothesis and the alternative hypothesis for one-sided and two-sided one-sample t-tests?

Answer 16

Two-sided one-sample t-test:

H0: the true mean is (x)

H1: the true mean isn’t (x)

One-sided one sample t-test:

H0: the true mean is x or less (or more if the other way)

H1: the true mean is above x

Question 17

What is the R command for one-sided t-tests in R?

Answer 17

t.test(x, y, alternative=”greater”)

x = sample mean

y = theorised mean

alternative = ‘greater’ or ‘less’ depending on direction

Question 18

When do you use an independent samples t-test?

Answer 18

When comparing two groups

Question 19

How do you write the null hypothesis and alternative hypothesis for independent samples t-tests?

Answer 19

Question 20

What assumptions are made in an independent samples t-test?

Answer 20

population distributions are normal

observations are independently sampled

groups have the same standard deviation

(a.k.a. “homogeneity of variance”, “homoscedasticity”)

Question 21

What is the diagnostic test statistic for independent samples t-tests?

What is the sampling distribution?

Answer 21

test statistic: t

Sampling distribution: t, with N1+N2-2 degrees of freedom

Question 22

If the null hypothesis is true in an independent sample t-test, what should the sampling distribution of t be?

Answer 22

Close to 0

If different, substantially different from 0

Question 23

Student t-test assumes what about variance?

Answer 23

Equal variance

Question 24

What is the R command for a student t-test?

Answer 24

t.test( price ~ colour, wines, var.equal=TRUE )

just like independent samples but with added variance

Question 25

What is the R command for an independent samples t-test?

Answer 25

independentSamplesTTest( x ~ y, z )

x ~ y are groups comparing

z is data set

Question 26

The Welch t-test assumes what about variance?

Answer 26

Not equal variance

(much safer thing to do)

Question 27

How does the Welch t-test adjust for not having equal variance?

Answer 27

“Effective” degrees of freedom is adjusted to be a bit smaller, depending on just how unequal the sample standard deviations are (not necessarily a whole number)

Question 28

R command for Welch t-test?

Answer 28

t.test (price~colour, wines)

• Price~colour = the formula that describes our test, to see if price is related to colour*
• Wines = the dataset that the formula is taken from*

Question 29

What are the important test results to report for a Welch t-test?

Answer 29

The test statistic, degrees of freedom, p-value, effect size and confidence interval (for the difference between means)

Question 30

What is the command in R for a one-sided two-sample t-test?

Answer 30

t.test(price ~ colour, wines, alternative=”less”)

Question 31

What is a z-score?

Answer 31

They reflect the distance from the mean in terms of standard deviations

e.g. z-score of +2 means it is 2 standard deviations above the mean

Question 32

What does the test statistic (t) represent in t-tests?

Answer 32

Reflects the distance of your data from the mean

Question 33

Define: homoscedasticity

Answer 33

Same variance