T-tests Flashcards
In a dependent sample t-test, what is the first step?
Find the research and the null hypothesis in words and symbols
In a dependent means t-test, what is step 2?
Determine the characteristics of the comparison distribution
What are the characteristics of a comparison distribution?
Mean
Standard deviation
Shape
What is the comparison distribution for a dependant means t-test?
Distribution of means of difference scores
What is the mean in a dependent means t-test?
Mew sub M = Mew
How to find standard deviation in dependent means t-test
S^2 = SS / N-1
S = square root of S^2
SM = S / square root of N
What is the shape in a dependent means t-test?
A t-distribution with N-1 degrees of freedom
What is step three of dependent means t-test?
Determine the cutoff score on the comparison distribution
How to find the cutoff score on the comparison distribution table
Go to the column of the df (N-1)
Go to the row of alpha (assume .05 if not given)
Find matching cutoff score
What is step four of dependent means t-test?
Determine the score of your sample on the comparison distribution of the means of difference scores
Find t
How to solve for t
t = M - mewM / SM
What is step 5 of dependent means t-test?
Determine whether or not to reject the null
- if the score of your sample falls further than the cutoff score then you reject the null.
Step one of single sample t-test
State the populations and a research and null hypothesis as words and symbols
Symbol version of population one
Mew 1
Mew 1 in words
Population one
Population two as symbols
Mew 2
Mew 2 as words
Population two
Null hypothesis for a single sample t-test
Mew 1 = Mew 2
What does the population 1 consist of in a single sample t-test?
The population being studied
What does the population 2 consist of in a single sample t-test
The general population
Research hypothesis in single sample t-test
Mew 1 does not equal Mew 2
What is step two in a single sample t-test?
Determine the characteristics of the comparison distribution
What are the characteristics of a comparison distribution in a single sample t-test?
Mean
Standard deviation
Shape
What is the comparison distribution for a single sample t-test?
Distribution of means
When you have 2 sets of means for each person in a dependent means t-test, what should you do?
Combine the means to make a difference score for each person
How to calculate a difference score for a dependent means t-test
Score 2 - score 1 (after - before)
Mean of difference scores = MD
How to calculate deviation for a dependent means t-test
D - MD
Difference score - the mean of difference scores
How to calculate squared deviation in a dependent means t-test
Square the deviation in the previous column
SSD = sum of squares D
How to find SSD (Sum of Squares D)
Add together all of the squared deviations
What is the research hypothesis for a dependent means t-test?
Research shows an increase = Mew after - Mew before > 0
- difference scores are greater than 0
What is the null hypothesis for a dependent means t-test?
The mean of the population of difference scores = 0
- no difference
- or an effect in the opposite direction of the research hypothesis
What is the mean symbol in a single sample t-test?
Mew sub M
= Mew
Calculate standard deviation in a single sample t-test
USE SAMPLE VARIANCE WHEN POPULATION VARIANCE ISN’T GIVEN!
Sigma sub M = sigma / square root of N
OR
SD^2 = SS / N
OR
S^2 = SS / N - 1 or SS / df
Formula for estimated population variance
S^2 = SS / N-1
Estimate of the population standard deviation
S = square root of S^2
Estimated standard deviation of the distribution of means
SM = S / square root of N
What is the shape of the comparison distribution in a single sample t-test?
T-distribution with N-1 df
T-distribution
When the df is higher, the distribution shape looks more normal
When the df is lower, the distribution shape looks more heavy tailed
Step three of single sample t-test
Determine the cutoff sample score using a t table
Step four of single sample t-test
Determine where the sample score falls on the comparison distribution
- goes on each side of the curve
How to find t for a single sample t-test
t = ( M - Mew sub M ) / SM
In a single sample t-test, which side of the curve do we put the cutoff score?
Both sides (one negative and one positive)
Step five of single sample t-test
Decide whether or not to reject the null
How do you know to reject the null in a single sample t-test?
If the sample score is different to the cut off score
What is the comparison distribution for a t-test for independent means?
A distribution of differences between means
How to calculate comparison distribution for a independent means t-test
Take the mean of the experimental groups distribution of means
Take the mean of the control groups distribution of means
Subtract the control group from experimental group to get difference between means
Three characteristics of a comparison distribution in independent means t-test
Mean
Shape
Standard deviation
Find the mean in an independent means t-test
Mew M1-M2 = 0
Find the shape of the comparison distribution for an independent means t-test
T-distribution with df total
How to calculate df total
df total = df1 + df2
- df1 = N1-1
- df2 = N2-1
What is the standard deviation for an independent means t-test
Standard deviation = Sdifference
Sdifference
Independent means t-test
- S1^2 = SS1 / N1-1 and S2^2 = SS2 / N2-1
- S^2pooled = [df1 / df total (S1^2) ]+[df2 / df total (S2^2) ]
- SM1^2 = S^2pooled / N1 and SM2^2 = S^2pooled / N2
- S^2 difference = SM1^2 = SM2^2
- S difference = square root of S^2 difference
If there are 10 volunteers and I randomly assign half of them to each group, what’s the N of each group?
Independent means t-test Q
N1 = 5
N2 = 5
For each sample in an independent means t-test, what should I calculate?
The mean and the sum of squares for each
What is population one in an independent means t-test?
The experimental population/ group
What is population two in an independent means t-test?
The control population/ sample group
What is the research hypothesis in an independent means t-test?
Pop1 < Pop2
OR
Pop1 > Pop 2
What is the null hypothesis in an independent means t-test?
The opposite to the research hypothesis
Step three of an independent means t-test
Find the cutoff score on the comparison distribution
How to find the cutoff score of the comparison distribution
One or two tailed test?
df = ?
Alpha = ? (assume .05 if not told)
Step four of an independent means t-test
Score of the sample on the comparison distribution
Score of the sample on the comparison distribution
t = [(M1 - M2) / Sdifference ] - 0
Step five of an independent means t-test
Decide whether to reject the null
How do you reject the null in an independent means t-test?
If the sample score is more extreme than the cutoff score
Effect size
The difference between the population means divided by the population’s standard deviation
d = (mew1 - mew2) / sigma
Calculate estimated d
d = (mew1 - mew2) / Spooled
Effect size conventions
.20 = small
.50 = medium
.80 = large
Find power in an independent means t-test
Decide if it’s a one or two tailed test
Find N overall (2 groups of 5 = 10)
What is the effect size?
