t-Tests Flashcards
Degrees of Freedom?
- n - 1
- Example, You have n numbers that must sum to 10
- x1 + x2 + x3 + x4 = 10
- First choice: you choose x1 = 13
- Then, x2 + x3 + x4 = -3
- Second choice: you choose x2 = 8
- Then, x3 + x4 = -11
- Third choice: you choose x3 = 3
- Then, x4 = -14 (forced, no choice can be made)
- You were able to make 3 choices before the 4th decision was forced, or you were able to make n-1 choices
SEM
- Standard Error of the Mean
- S / sqrt(n) ; where S = sample standard deviation
T-statistic?
- t = (xbar - M) / SEM
- the T-statisitic is used in a T-test when you are deciding if you should support or reject the null hypothesis
- it is very similar to the z-score
- you should use the T-statistic when you have a small sample size (less than 30), or if you don’t know the population standard deviation
- the greater the T value, the more there is evidence your score is different from the average
- a smaller T value is evidence that the score is NOT significantly different from the average.
ME
- Margin of Error
- ME = tcritical * SEM
CI
- Confidence Interval
- CI = xbar +/- ME
Cohen’s d
- standarized mean difference that measures the distance between means in standardized units
- What is mean difference? (xbar - M)
- What is S?
- Standard deviation of the sample
- Cohen’s d = xbar - M / S
r2
- coefficient of determination
- 0.00 to 1.00
- Value of ‘0’ means that the variables are not at all related
- Value of ‘1’ means that the variables are perfectly related
- This rarely happens
- df = degrees of freedom
- r2 = t2/t2 + df
- NOTE: ‘t’ is not tcritical ; it is the t-value you get from the t-test
Dgrees of freedom for a 2-dimensional array?
- (n - 1)2
- Example for a 4x4 array, you can make (4-1)2 choices, or 9 choices
What is the major difference between the T-score and the Z-score?
- The major difference between using a Z-score and T-score is that you have to estimate the population standard deviation with a T-score
- The T-test is also used if you have a small sample size (less than 30)
What is the t-critical value for a one-tailed alpha levle of 0.05 with 12 degrees of freedom?
- t-table
- 1.782
You have a sample of size 30. What are the t-critical values for a two-tailed test with a = 0.05?
- t-table
- Since it is a two-tailed test, you want to look for .025 with degrees of freedom of (n - 1) or 29
- 2.045
Your sample is size 24 and you get a t-statistic of 2.45.
The area to the right of the t-statistic is between __________ and _________ ?
- (n - 1) = 23
- t-table
- Consulting the table for 23 degrees of freedom, 2.45 is between the t-statistics of 2.177 and 2.500
- The t-statisitc of 2.177 aligns with a p-value of 0.02
- The t-statistic of 2.500 aligns with a p-value of 0.01
- So, the area to the right of the t-statisitc is between 0.02 and 0.01
If the t-statisic is “far from” the popultaion mean, what do you do?
- reject the null
The LARGER or SMALLER the value of xbar, the stronger the evidence that M > Mo
- Larger
The LARGER or SMALLER the value of xbar, the stronger the evidence that M < Mo
- Smaller
The further the value of xbar from Mo in either direction, the STRONGER or WEAKER the evidence that M != Mo
- Stronger