Task 4

Question 1

Discuss one sample t-test vs paired sample t-test

Answer 1

• > computationally the same (see formula)

- > paired is just one sample t test but performed on a set of difference scores (d)

Question 2

Is the independent t-test computationally the same as one sample and paired sample?

Answer 2

no

Question 3

How to create a confidence interval for a one sample t-test?

Answer 3

same as z test just replace z* with t*

Question 4

p-values are only exact when the distribution is

Answer 4

normal

Question 5

p-values are normally distributed when

Answer 5

the Ho is true

Question 6

Why is it important to use the right distribution?

Answer 6

The whole point of using the correct distribution (normal, t, f, chisq, etc.) is to transform from the test statistic to a uniform p-value. If the null hypothesis is false then the distribution of the p-value will (hopefully) be more weighted towards 0.

Question 7

What does the usefulness of t-tests depend on?

Answer 7

results of a one-sample t-test are exactly correct only when population = exactly normal which real populations never are, therefore usefulness of t procedures depends on how strongly they are affected by non-normality (robust - not strongly affected)

Question 8

What are t-procedures

a) robust against
b) not robust against

Answer 8

a) robust against non-normality of the population except in case of outliers or strong skewness
b) not robust against outliers because sample mean x and sample standard deviation are not resistant to outliers

Question 9

How can you improve the p-value accuracy and critical value accuracy from t distributions when population is not normal

Answer 9

large n

Question 10

How to increase confidence level?

Answer 10

increase z*

Question 11

What is pooled standard deviation? (Sp)

Answer 11

combination of sample standard deviations, used when equal variances assumed

Question 12

What is Levenes test?

Answer 12

tests if Ho: variance of samples equal

if largest s/smallest s is less than 2, we assume equal variances therefore use pooled independent samples t test

Question 13

What distribution is required to conduct a one samples t-test?

Answer 13

sample must be drawn from a normally distributed population

• > if population is normal, sampling distribution will be normal
• > make sure sample is large enough if violated, the sampling distribution will then become approx normal due to CLT

Question 14

How do we know whether to conduct a z-test or t-test?

Answer 14

for z-test the population stnadard deviation is known

for t-test the population standard deviation is not known therefore we use a sample standard deviation

Question 15

How many random variables are involved in a t-test?

How does this affect the distribution?

Answer 15

2, the sample standard deviation and sample mean as these vary among different samples

-> distribution becomes more dispersed

Question 16

How can you improve the efficiency (accuracy) of a sample standard deviation (which is an estimate) for t-tests?

Answer 16

large n, will resemble more and more as an average deviation causing dispersion to decrease approaching almost a normal z-distribution

Question 17

Which is less reliable and powerful, z-test or t-test and why?

Answer 17

t-test is less powerful as the distribution is broader (standard deviation used is an estimate)

Question 18

What does a t-test assume about the variable in the study and what to do if violated?

Answer 18

assumes its quantiative e.g. number of socks

-> if violated then use X^2 goodness of fit

Question 19

Why do we use degrees of freedom?

Answer 19

to make up for lowered reliability (bigger the sample, more reliable)

Question 20

Since all t-values are positive, what do you do if you get a negative one?

Answer 20

just search the same number but positive, the p-values are the same as the t-distribution is symmetric

Question 21

How do you calculate the degrees of freedom for

a) one sample t test
b) paired samples t test
c) independet samples t test (variances assumed and unassumed)

Answer 21

a) n-1
b) n-1
c) assumed -> n1+n2-2
unassumed -> (lowest ni)-1

Question 22

Both samples in a paired samples t-test are…

a) independent or
b) dependent

Answer 22

b

Question 23

Paired samples t-test is a
a) within subjects design or
b) between subjects design
why?

Answer 23

within subjects design

• > repeated measures of the same person
• > pairs of people matched

Question 24

What is the difference between paired samples t-test and independent samples t-test

Answer 24

in paired samples they are dependent hence a within subjects design (repeated measures of the same person, pairs of people matched)

in independent samples they are independent hence between subjects

Question 25

What is correlation like in paired samples t tests?

Answer 25

high

Question 26

When is a t-statistic

a) normally distributed
b) has a t distribution

Answer 26

a) when n is greater than 25 -> use z table

b) when n is less than 25 -> use t table

Question 27

Why don’t we have equal variances in paired but in independent?

Answer 27

paired is to measure differences so we need variation therefore assume unequal variation

Question 28

How to find t*?

Answer 28

you need the df and p-value, then given in t-table

Question 29

In a paired samples t-test, what kind of variable are subjects paired on?

Answer 29

a within-subjects variable e.g. IQ

gender, for example, is a between-subjects variable

Question 30

Differentiate between a within-subjects and between-subjects variable

-> when do we use each one?

Answer 30

Within-subjects variable: an independent variable that is manipulated by testing each subject at each level of the variable.
-> paired t-tests

Between-subjects variable: different groups of subjects are used for each level of the variable.
-> independent samples t-test

Question 31

What marks the threshold?

Answer 31

x-bar *