The independent groups t-test Flashcards
How do you work out the variance?
s.d. ^2
What is the formula for independent groups t-test?
t = (mean A - mean B) / SQRT (e.s.e. (A)^2 + e.s.e. (B)^2)
Samples (size N = 16) are repeatedly taken from two normal populations (A and B) with known parameters:
A = N(25, 10)
B = N(35, 15)
On each occasion, the difference in sample means, m(B) - m(A), is calculated.
a) The standard error of the mean for population A is: s.e.(A) =
b) The standard error of the mean for population B is: s.e.(B) =
c) The variance for population A is: var(A) =
d) The variance for population B is: var(B) =
e) The quantity sqrt( var(A)/N + var(B)/N) is:
f) The quantity sqrt( se(A)^2 + se(B)^2 ) is:
g) The theoretical population mean of the sampling distribution of differences in sample means (B-A) is:
h) The theoretical population s.d. of the sampling distribution of differences in sample means (B-A) is:
a) 2.50
b) 3.75
c) 100.0
d) 225.0
e) 4.51
f) 4.51
g) 10.0
h) 4.51
Samples (size N = 25) are repeatedly taken from two normal populations (A and B) with known parameters:
A = N(22, 5)
B = N(25, 6)
On each occasion, the difference in sample means, m(B) - m(A), is calculated.
a) The standard error of the mean for population A is: s.e.(A) =
b) The standard error of the mean for population B is: s.e.(B) =
c) The variance for population A is: var(A) =
d) The variance for population B is: var(B) =
e) The quantity sqrt( var(A)/N + var(B)/N) is:
f) The quantity sqrt( se(A)^2 + se(B)^2 ) is:
g) The theoretical population mean of the sampling distribution of differences in sample means (B-A) is:
h) The theoretical population s.d. of the sampling distribution of differences in sample means (B-A) is:
a) 1.0
b) 1.2
c) 25.0
d) 36.0
e) 1.56
f) 1.56
g) 3.0
h) 1.56
Samples (size N = 30) are repeatedly taken from two normal populations (A and B) with known parameters:
A = N(12.51, 2.3)
B = N(13.63, 2.4)
On each occasion, the difference in sample means, m(B) - m(A), is calculated.
a) The theoretical population mean of the sampling distribution of differences in sample means (B-A) is:
b) The theoretical population s.d. of the sampling distribution of differences in sample means (B-A) is:
a) 1.12
b) 0.61
You wish to test the research hypothesis that left-handedness is accompanied by different levels of accuracy to right-handedness in throwing an object at a target using a preferred hand. You conduct an experiment in which a left-handed group of 26 participants and a right-handed group of 26 participants both throw a dart at a target from a fixed distance of 30cm. You measure the deviation of the dart from the target (in mm). The data in the two groups are summarised below:
Right-handed group: m = 12.51, s = 2.3
Left-handed group: m = 13.63, s = 2.4
a) The e.s.e. for the right-handed data, e.s.e.(R), is:
b) The e.s.e. for the left-handed data, e.s.e.(L) is:
c) The difference in sample means is (L-R):
d) The quantity sqrt(e.s.e.(L)^2 + e.s.e.(R)^2 ) =
e) The appropriate t-statistic to test the 2-tailed hypothesis stated above is:
f) Based on the statistic in e) should you reject or fail to reject the null hypothesis?
a) 0.45
b) 0.47
c) 1.12
d) 0.65
e) 1.72
f) Fail to reject
You wish to test the research hypothesis that people with green eyes have more REM sleep. You conduct an experiment in which a green eye group of 31 participants and a non-green eye group of 31 participants spend a night in a sleep lab and standard electro-oculography (EOG) methods are used to measure REM. The data in the two groups are summarised below:
Green eye group: m(green) = 254.34, var(green) = 806.56
Non-green eye group: m(non-green) = 234.51, var(non-green) = 1056.25
a) The difference in sample means (green eye minus non-green eye) is:
b) The quantity sqrt( var(green)/N + var(non-green)/N ) =
c) The appropriate t-statistic to test the 1-tailed hypothesis stated above is:
d) Based on the statistic in c) should you reject or fail to reject the null hypothesis?
a) 19.83
b) 7.7518
c) 2.56
d) Reject
When do we use paired/repeated t-tests?
When data in both conditions can be naturally paired
e.g. repeated measures, pre-post etc
When do we use independent groups t-tests?
When data in both conditions cannot be paired
e.g. between subjects, quasi-experimental design
Which t-test involves converting the 2 samples from conditions A and B into one sample by taking the difference between the paired data?
Paired/repeated t-test
Once we have found the mean difference between groups A and B, what can we calculate? List 3
1) a sample means over differences:
mD = mA – mB
2) sample s.d. over differences: sD
3) e.s.e. over differences: eseD = sD/√N
When testing a hypothesis regarding the difference between sample means in two conditions:
If you have a within-participants design you would use a (………….) t-test.
Conversely, if you have a between-participants design, you would use a (…………….) t-test.
1) Paired/related
2) Independent groups
The t-statistic generated when testing hypotheses about differences between sample means in two conditions is given by the (…………) the sample means divided by a measure of (………….) observed in the two conditions.
1) Difference between
2) Variability
In the case of a paired t-test, the data in the two samples is converted into a single sample of data by taking the (………..) paired scores.
1) Difference between
The variability required to scale the difference in sample means in this case is just the standard error associated with the difference scores.
The paired t-test is then equivalent to a (…………) on the difference scores.
1) One-sample t-test
