t-test

Question 1

t-test

Answer 1

• when we have 1 IV with 2 levels
• estimates whether the population means under the 2 levels are different
• estimates based on difference between the measured sample means

Question 2

independent t-test

Answer 2

between participants / independent groups

Question 3

paired t-test

Answer 3

within participants/ repeated measures

Question 4

true experimental

Answer 4

random allocation

Question 5

variance between IV levels

Answer 5

variance we assume is accounted for by manipulation of IV

Question 6

variance within IV levels

Answer 6

difference between participants within the groups (levels)
- reflected by standard deviation

Question 7

how does variance between IV levels arise

Answer 7

• manipulation of IV
• individual differences
• experimental error

Question 8

experimental error

Answer 8

random or constant

Question 9

random error

Answer 9

chance fluctuation in measurement
e.g. hitting stop watch too early or late

Question 10

constant error

Answer 10

confounds that influence measurement of DV between IV levels
- bias
e.g. giving one group practice and one group not

Question 11

sources of variance within IV levels

Answer 11

• individual differences
• experimental error (random not including constant)

Question 12

null hypothesis

Answer 12

• no difference between the population means and sample means
• H0: u1-u2=0
  or
  u1=u2

Question 13

what does t-distribution represent

Answer 13

• distribution of sampled mean differences when the null hypothesis is true

Question 14

features of t-distributions

Answer 14

• mean of 0
• ## s.d. = s.e

Question 15

s.e.

Answer 15

standard error
the extent to which an individual sampled mean difference deviates from 0

Question 16

t-value

Answer 16

difference between sample means
reflected in standard error units

(don’t need to memorize formula)

Question 17

ESEd

Answer 17

s=variance
n=sample size

Question 18

t-value closer to 0

Answer 18

small variance between IV levels relative to within IV levels

Question 19

t-value further from 0

Answer 19

larger between IV levels than within IV levels
- shows difference of manipulation of IV

Question 20

in order to claim value of t is significant…

Answer 20

it must fall outside of the 95% bounds, in the 2.5% tails

Question 21

if t > critical value

Answer 21

reject the null

Question 22

larger degrees of freedom

Answer 22

more reliable the estimate

Question 23

d.f. fro 2 sample independent t-test

Answer 23

Question 24

what is t-distribution mediated by

Answer 24

degrees of freedom

Question 25

assumptions of independent t-tests

Answer 25

- normality - homogeneity of variance - equivalent sample sizes - independence of observations

Question 26

normality - independent

Answer 26

DV should be normally distributed, under each level of IV

Question 27

homogeneity of variance

Answer 27

the variance in the DV, under each level of the IV, should be reasonably equivalent - check using Levene's test in SPSS

Question 28

Levene's test

Answer 28

SPSS - we want a non-significant result - under H0: no difference between variances under each level of IV (homogeneity) - but it p<0.05 we reject null - heterogeneity - use row below is violated

Question 29

independence of observtions

Answer 29

scores under each IV level should be independent

Question 30

what do we do if we violate assumptions of independent t-test

Answer 30

Mann-Whitney U test

Question 31

p

Answer 31

reject null

Question 32

how to get a t-test result from SPSS output

Answer 32

Question 33

paired t-test

Answer 33

- related/ dependent t-test - used for within-subjects/ repeated measures design

Question 34

t calculation for paired

Answer 34

don't need to memorize

Question 35

what contributes to variance for within-subjects design

Answer 35

- experimental error - manipulation of IV

Question 36

assumptions of paired t-test

Answer 36

- normality - sample size roughly equal

Question 37

normality - paired

Answer 37

- distribution of difference scores between IV levels should be aprox. normal - ok to assume if n>30

Question 38

non-parametric equivalent of paired t-test

Answer 38

Wilcoxon T test - if assumptions are violated

Question 39

paired t-test: SPSS output

Answer 39

Question 40

degrees of freedom for paired t-test

Answer 40

df = ( n - 1)

Question 41

effect size measure

Answer 41

Cohen's d

Question 42

Cohen's d

Answer 42

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

Question 43

Cohen's d formula

Answer 43

... ignore the sign (remove negative sign) - express to 2 d.p

Question 44

interpreting Cohen's d effect size

Answer 44

e.g. bigger effect size, further apart population means, less overlap

Question 45

t

Answer 45

magnitude of difference between two IV level means, expressed in ESE units

Question 46

why t not Cohen's d

Answer 46

takes sample size into account

Question 47

t-test design write up

Answer 47

- IV: levels, subjects design (between or within), steps taken to eliminate confounds (random allocation for IT or counterbalancing for paired) - DV: what was measured

Question 48

t-test results write up: step 1: descriptive statistics in the table

Answer 48

in table put: - measure of central tendency as mean - measure of spread: standard deviation - interval estimates: 95% confidence interval around mean (upper and lower)

Question 49

t-test results write up: step 2: results of inferential statistics

Answer 49

- Descriptive statistics are reported in table 1 - state test used (paired of independent t-test) and what it revealed e.g. an independent t-test revealed that dog owners told that their dog showed potentially were significantly quicker to complete the course than those owners told their dog had no potential, - state test statistic as t(df) = _.__, p = .__ - if needed (equal variances not assumed) - state if result was significant and direction of significance (which IV was higher) - mean difference and 95% CIs around mean difference - the effect size: Cohen's d (if significant report as small, medium large, if not significant report alongside t statistic after p value) - - e.g. the mean time difference was 87.80 seconds (95% CI [x,x], demonstrating a large effect size, d = X.

Question 50

discussion

Answer 50

summary of findings with no statistical jargon e.g. no significant - provide direct answer to research question e.g. paired- we found evidence of an impact of alcohol consumption of students' performance on an arcade game. e.g. independent- dog owners advised their dog showed agillity potential achieved faster course completion than those advised their dog did not showe potential. Manipulatin the information given to the owners about their dog's agility potential appears to have influenced their later agility performance