Section 5 (p59 - 68)

Question 1

When is student’s t distribution used?

Answer 1

Population standard deviation is unknown
Population is normally distributed
Independent items

Question 2

What is the parameter of student’s T distribution?

Answer 2

Number of degrees of freedom

Question 3

What does the degrees of freedom equal?

Answer 3

n-1

Question 4

What does the standard error equal for student’s t distribution?

Answer 4

s/ square root of n

Question 5

How many t distributions are there?

Answer 5

An infinite number

Question 6

What happens, in terms of the normal and the t distribution, as the size of the sample increase?

Answer 6

t distribution approximates the normal more closely

Question 7

What does the critical values depend on in the t distribution?

Answer 7

The sample size and significance level

Question 8

Where can critical values for the t distribution be found?

Answer 8

Tables or the internet

Question 9

In practice, what test statistic is used to test means?

Answer 9

t

Question 10

What type of t-test is done when you are comparing a hypothesis about a population mean with unknown standard deviation against a reference?

Answer 10

One-sample T-test

Question 11

What is the symbol for the critical value at the c% confidence level for the t distribution with n-1 degrees of freedom?

Answer 11

tn-1,c e.g. t19,0.99

Question 12

What are the 3 types of t-tests?

Answer 12

One-sample
Paired/ dependent
Un-paired/ independent

Question 13

How does a one-sample T test differ from a test when the population standard deviation is known?

Answer 13

Instead of using the z statistic with set critical values for the confidence interval, the t statistic is used and critical values are determined from the probability distribution function

Question 14

What is another name for dependent observations?

Answer 14

Paired observations

Question 15

Name for type of observation when repeated observations are made on the same individuals?

Answer 15

Dependent

Question 16

Name for type of observation when treatment is applied to different individuals?

Answer 16

Independent

Question 17

What is the principal source of variation of response to a treatment?

Answer 17

Between-subject differences

Question 18

How can between-subject differences be eliminated entirely?

Answer 18

By applying both treatments to the same individual

Question 19

How can between-subject differences be reduced?

Answer 19

By matching for factors known to affect the outcome

Question 20

In trials where matching of factors known to affect outcomes occurs, are the outcomes dependent or independent?

Answer 20

Dependent

Question 21

Other name for a dependent T test?

Answer 21

Paired T test

Question 22

In comparison of dependent continuous data distributions, what are inferences based on?

Answer 22

The mean difference

Question 23

Symbol for the mean difference?

Answer 23

d with a line above it

Question 24

Can inferences using the mean difference be based on the t distribution?

Answer 24

Yes, providing the differences are plausibly normally distributed

Question 25

What is a hypothesis test of the equality of 2 independent sample means normally doing?

Answer 25

Testing if the samples have been drawn from the same (plausibly normal) population

Question 26

How can an estimate of the variance of the population be obtained for an independent t test?

Answer 26

When the sample variances are comparable (not significantly different) they can be pooled

Question 27

Should you still do an independent t test if the sample variances are not comparable?

Answer 27

Exercise caution doing this as clearly the samples are not drawn from the same population

Question 28

What are the 4 options when considering doing an unpaired T test if the sample variances are not comparable?

Answer 28

Investigate the relationship between means and variances (use a logarithmic transformation)
Use Welch’s modified T test
Use a non-parametric test to compare the means
Do not proceed with the test of the means

Question 29

Why does a logarithmic transformation sometimes help achieve equality of variances for an unpaired T test?

Answer 29

In some cases, the variability of a measurement increases with magnitude

Question 30

Name the approximation to a t test when samples are known to have arisen from normal distributions with unequal variances?

Answer 30

Welch’s test

Question 31

What distribution is formal tests of the equality of two variances based on?

Answer 31

The F distribution

Question 32

What is the f statistic equal to?

Answer 32

s1 squared / s2 squared

Question 33

What are the 2 parameters of the f statistic?

Answer 33

n1 - 1 and n2- 1

Question 34

How do you decide which variance is s1 squared and which is s2 squared for the f statistic?

Answer 34

s1 squared is the larger variance

Question 35

How are the results of the f statistic interpreted?

Answer 35

Significance of the f statistic can be established from tables
If F is not significant, the variances are comparable and population variance can be calculated

Question 36

What does the 95% confidence interval for the differences between the sample means equal?

Answer 36

Observed difference between means +/- tn1+n2-2 X standard error of difference (get these equations from test statistic of independent t-test)