t tests

Question 1

when is a t test used?

Answer 1

when we have one IV with 2 levels

Question 2

what does a t-test do?

Answer 2

estimates whether the population means under the 2 levels of the IV are different

Question 3

assessing differences using samples

Answer 3

• XA - XB = XD
• determine XD for every sample
• plot all these mean differences
• the samples mean differences would build toward

a normal distribution, with a mean equivalent to the true population mean difference (UD)
-sampling distribution of differences

Question 4

sampling distribution of differences

Answer 4

• null hypothesis (H0) states that there is no difference between population means
  -H0: U1-U2= 0
  -H0: U1=U2
• under the null hypothesis, the sampling distribution of differences will have a mean of 0
• T distribution represents the distribution of samples mean differences when the null hypothesis is true

Question 5

t distribution

Answer 5

• Has a mean of 0
• The extent to which an individual samples mean difference deviates from 0
  -can be expressed in standard error unit
• We can convert the difference between our sample means (XD) into a t value, by expressing the difference in SE units

Question 6

standard error of differences

Answer 6

• To convert XD to t we need to know the SE of the sampling distribution of the mean (SED)
  distribution is hypothetical, would never measure the difference for all possible samples from the population
• We can estimate the SED based on the sample standard deviations (s) and sample sizes (n)

Question 7

T distribution: if the null hypothesis is true

Answer 7

95% of samples t values will fall within the 95% bounds of the t distribution
only 5% of samples will fall outside of the 95% bounds

Question 8

if the magnitude of the obtained t-value is smaller than the critical value of t

Answer 8

we fail to reject H0

Question 9

if the magnitude of the t value is smaller than the critical value of t, we reject H0

Answer 9

we reject H0

Question 10

degrees of freedom

Answer 10

The difference between the number of measurements made and the number of parameters estimated

Question 11

the larger the degrees of freedom in an estimate…

Answer 11

the more reliable the estimate

Question 12

degrees of freedom and the t distribution

Answer 12

The t distribution is mediated by degrees of freedom

Used to determine critical values

Question 13

p value

Answer 13

the probability of obtaining a t-value of a given magnitude when H0 is true

Question 14

alpha value

Answer 14

the threshold value we measure p against

Question 15

if p< or = a

Answer 15

reject the null hypothesis

Question 16

if p>a

Answer 16

reject the null hypothesis

Question 17

RMs to use independent t test

Answer 17

between participants/ independent groups

Question 18

what is variance effected by (independent)

Answer 18

manipulation of the IV (treatment effects)

individual differences

experimental error
-random error
-constant error

Question 19

t ratio

Answer 19

• Reflects the difference between the sample means, expressed in standard error units
• Can use the t-distribution to determine the probability of measuring a t-value and of the magnitude obtained (or greater), if the null hypothesis were true

Question 20

variance when t value close to 0

Answer 20

small variance between IV levels, relative to within IV levels

Question 21

variance when t value further away from 0

Answer 21

large variance between IV levels relative to within IV levels

Question 22

assumptions of independent t test

Answer 22

• The DV should be normally distributed, under each level of the IV
• Homogeneity of variance
• Equivalent sample size
• Independence of observations

Question 23

homogeneity of variance

Answer 23

the variance in the DV, under each level of the IV should be (reasonably) equivalent

Question 24

how to test homogeneity of variance (SPSS)

Answer 24

SPSS check with Levene’s test

Null hypothesis: there is no difference between the variance under each level of the IV (homogeneity)

if p<=0.05 we reject the null hypothesis (heterogeneity)

Question 25

non parametric equivalent of independent test

Answer 25

Mann-Whitney U test

Question 26

RMs to use paired test

Answer 26

within participants/ repeated measures

Question 27

variance in paired t test is effected by

Answer 27

manipulation of IV (treatment effects)

experimental error
-random error

Question 28

why is variance due to individual differences absent in paired tests

Answer 28

each participant acts as their own control

Question 29

assumptions of the paired t test

Answer 29

• Normality: the distribution of difference of scores between the IV levels should be approximately normal
  -assume okay if n>30
• Sample size: sample size under each level of the IV should be roughly equal

Question 30

non parametric equivalent of paired t test

Answer 30

wilcoxon t test

Question 31

if the effect of the IV is consistent

Answer 31

result is likely to be significant

Question 32

if the effect of the IV is not consistent

Answer 32

the result is likely to not be significant

Question 33

cohen’s D

Answer 33

the magnitude of difference between two IV level means, expressed in standard deviation units

standardised value expressing the difference between the IV level means
ignores sample size

Question 34

d= 0.2

Answer 34

small effect

Question 35

d= 0.5

Answer 35

medium effect

Question 36

d= 0.8

Answer 36

large effect