T-test Flashcards
Used when we have 1 IV with 2 levels
a. one-way ANOVA
b. t-test
c. two-way ANOVA
b. t-test
What does the t-test estimate?
Estimates whether the population means under the 2 levels of the IV are different
Estimates whether the population means under the 2 levels of the IV are different
a. one-way ANOVA
b. t-test
c. two-way ANOVA
b. t-test
Independent t-test is for…?
a. Between subjects
b. Within subjects
a. Between subjects
Paired t-test is for…?
a. Between subjects
b. Within subjects
b. Within subjects
Used when we have 1 IV with 2 levels, between subjects
Independent t-test
Used when we have 1 IV with 2 levels, within subjects
Paired t-test
A researcher recruited 90 dogs and their owners to take part in an agility challenge.
Before the challenge began, she told half the owners (chosen at random) that their dog showed positive signs of agility potential, and the other half that their dog did not show potential.
She then timed how long it took each dog-owner pair to complete the agility course
What are the…?
a. IVs
b. IV levels
c. DV
d. Subjects design
e. Type of test
a. Expectation of potential
b. 2 (potential, no potential)
c. Agility performance (time to complete agility course)
d. Between subjects
e. Independent t-test
What contributes to variance between IV levels in independent t-test?
List 3 things
- Manipulation of IV (treatment effects)
- Individual differences
- Experimental error; random error and constant error)
What contributes to variance within IV levels for independent t-tests?
List 2 things
- Individual differences
- Experimental error; random error)
True or False?
Manipulation of IV (treatment effects) contributes to variance between IV levels
True
True or False?
Manipulation of IV (treatment effects) contributes to variance within IV levels
False
Individual differences and experimental error (random error) contributes to variance between IV levels
What type of experimental error(s) contribute to variance between IV levels?
- Random error
- Constant error
What type of experimental error(s) contribute to variance within IV levelsfor indepdendent t-test?
- Random error
The t-distribution represents the distribution of sampled mean differences when…?
The null hypothesis is true
The t-distribution has a mean of …?
0
The extent to which an individual sampled mean difference deviates from 0 can be expressed in ______ units
Standard Error
What is the formula for differences in ESE ?
Diff. ESE = sqrt (SD a^2 + SD b^2) / (Sample size A + Sample size B)
True or False?
t is a ratio
True
t reflects the difference between ________ , expressed
in _______ units
The sample means
standard error
What can be used to determine the probability of measuring a t-value of the magnitude obtained (or greater), if the null hypothesis were true?
t-distribution
What is the formula for t
t = variance between IV levels / variance within IV levels
or
t = x difference / ESE difference
or
t = xA - xB / sqrt ((SDa^2 + SDb^2) / Na + Nb))
Is the variance between IV
levels relative to within IV levels large or small when t-value is close to 0?
Small
Is the variance between IV
levels relative to within IV levels large or small when t-value is further from 0?
Large
Small variance between IV
levels relative to within IV levels
t value is…?
a. Close to 0
b. Far from 0
a. Close to 0
Large variance between IV
levels relative to within IV levels
t value is…?
a. Close to 0
b. Far from 0
b. Far from 0
True or False?
If the null hypothesis is true, 5% of sampled t-values will fall within the 95% bounds of the t-distribution
False
If the null hypothesis is true, 95% of sampled t-values will fall within the 95% bounds of the t-distribution
True or False?
If the null hypothesis is true, 95% of sampled t-values will fall outside the 95% bounds (in the tails of the distribution)
False
If the null hypothesis is true, only 5% of sampled t-values will fall outside the 95% bounds (in the tails of the distribution)
If the magnitude of the obtained t-value is smaller than the critical value of
t, we…?
a. Fail to reject null
b. Reject null
a. Fail to reject null
If the magnitude of the obtained t-value is greater than the critical value of t, we …?
a. Fail to reject null
b. Reject null
b. Reject null
The difference between the number of measurements made and the number of
parameters estimated
sample size – no. parameters
This is known as…?
Degrees of Freedom
What is df?
The difference between the number of measurements made and the number of
parameters estimated
sample size – no. parameters
The larger the degrees of freedom in an estimate, the _____ the estimate
a. more reliable
b. less reliable
a. more reliable
The ______ the degrees of freedom in an estimate, the less reliable the estimate
a. Smaller
b. Larger
a. Smaller
What is the df for independent t-test?
df = n - 2
of
df = (nA-1) + (nB-1)
What are the 4 assumptions for independent t-test?
- Normality
- Homogeneity of variance
- Equivalent sample size
- Independence of observations
What is normality assumption for independent t-test?
The DV should be normally distributed, under each level of the IV
What is homogeneity of variance assumption for independent t-test?
The variance in the DV, under
each level of the IV, should be (reasonably) equivalent
How do we check the homogeneity of variance on SPSS?
Levene’s test
if p < 0.5, we reject the null, the variance is not homogenous
What is equivalent sample size assumption for independent t-test?
Sample size under each level of the IV should be roughly equal
What is independence of observations assumption for independent t-test?
Scores under each level
of the IV should be independent
What is the non parametric equivalent to the independent t-test?
Mann-Whitney U Test
Mann-Whitney U Test is the non parametric equivalent to a…?
Independent t-test
Do we ignore the +/- sign when reporting t-values?
Yes
What d.p. do you report t-values in?
2 d.p.
A student is convinced that he and his friends do better on their favourite arcade game when they are drunk than when they are sober.
To test this theory he records the scores of 50 friends playing the game on two occasions; once when
they are drunk, and once when they are sober (counterbalanced)
a. IV(s)
b. IV levels
c. DV
d. subject design
e. type of test
a. Alcohol status
b. 2 (sober, drunk)
c. Arcade game score
d. Within subjects
e. Paired t-test
Used for within subjects/repeated measures
designs
a. Paired t-test
b. Independent t-test
a. Paired t-test
What is the formula for t-ratio for paired t-test?
t = variance between IV levels / variance within IV levels
or
t = diff x (mean) / diff ese
What contributes to variance between IV levels in repeated measures design?
- Manipulation of IV (treatment effects)
- Experimental error
Why is there no variance due to individual differences in repeated measures design?
Because each participant acts as his/her own control
What contributes to variance within IV levels in repeated measures design?
- Experimental error
What are the 2 assumptions for paired t-test?
- Normality
- Sample size
What is the normality assumption for paired t-test?
The distribution of difference scores between the IV levels should be approximately normal
i.e. the calculated individual difference scores
What is the sample size assumption for paired t-test?
Sample size under each level of the IV should be roughly equal
What is the non parametric equivalent to a paired t-test?
Wilcoxon T Test
Wilcoxon T Test is the non parametric equivalent to…?
Paired t-test
When interpreting 95% CI plots for repeated measures, result is likely to be significant when…?
The difference between
means (size of effect) is modest but the effect is
consistent
The difference between
means (size of effect) is modest but the effect is
consistent
The result is likely to be…?
a. Significant
b. Not significant
a. Significant
When interpreting 95% CI plots for repeated measures, result is not likely to be significant when…?
The difference between
means (size of effect) is modest but the effect is not consistent
The difference between
means (size of effect) is modest but the effect is not consistent
The result is likely to be…?
a. Significant
b. Not significant
b. Not significant
True or False?
For repeated measures designs, you can determine if result is likely to be significant by looking at (95% CI plot)
False
For repeated measures designs, you cannot determine if result is likely to be significant by looking at (95% CI plot)
What is the formula to calculate t value on SPSS?
t = mean (of differences) / SE of mean (differences)
Do we report t-values less than 0 with a 0 in front of the decimal point?
e.g. .539 -> t = 0.54
Yes
What is the df for paired t-test?
df = N - 1
The magnitude of difference
between two IV level means, expressed in SD units
i.e. a standardised value expressing the difference between the IV level means
This is known as…?
Cohen’s d
What is cohen’s d?
The magnitude of difference
between two IV level means, expressed in SD units
i.e. a standardised value expressing the difference between the IV level means
What is the formula for cohen’s d?
d = difference between sample means / mean sample SD
or
d = meanA - meanB / ((SD A + SD B) / 2)
Calculate the cohen’s d for this:
Potential
Mean = 157.22
SD = 35.95
No potential
Mean = 245.02
SD = 32.87
d = meanA - meanB / ((SD A + SD B) / 2)
d = 157.22 - 245.02 / ((35.95 + 32.87) / 2)
d = 2.55
Do you ignore the +/- sign when reporting cohen’s d?
Yes
What d.p. do you report cohen’s d in?
2 d.p.
What is considered a small cohen’s d effect size?
0.2
What is considered a medium cohen’s d effect size?
0.5
What is considered a large cohen’s d effect size?
0.8
True or False?
Cohen’s d ignores sample size
True
The magnitude of difference between two IV level means, expressed in standard
deviation units
This is known as…?
a. t
b. Cohen’s d
b. Cohen’s d
The magnitude of difference between two IV level means, expressed in ESE units
This is known as…?
a. t
b. Cohen’s d
a. t
Ignores sample size
a. t
b. Cohen’s d
b. Cohen’s d
Qualifies the size of the effect in the context of the
sample size
a. t
b. Cohen’s d
a. t
On SPSS, cohen’s d is calculated differently from the formula used to calculate by hand
Which outcome will be very similar to hand calculation?
a. Between subjects (independent t-test)
b. Within subjects (paired t-test)
a. Between subjects (independent t-test)
On SPSS, cohen’s d is calculated differently from the formula used to calculate by hand
Which outcome may be quite different to hand calculation?
a. Between subjects (independent t-test)
b. Within subjects (paired t-test)
b. Within subjects (paired t-test)
