When do we use the t distribution?
-When we don’t know the standard deviation
Different t distributions for…?
Different sample sizes/degrees of freedom
The t distribution is _____ and _____ than the z distribution?
wider;flatter (especially with smaller samples sizes)
As sample size (n) and degrees of freedom approach infinity….?
The t distribution approaches the z distribution (looks more normal)
Degrees of Freedom
The number of scores that are free to vary when we estimate a population parameter from a sample (n-1)
What is the degrees of freedom for a 1 sample t-test?
n-1
Steps to use the t-table for hypothesis testing
1.) One or two tailed?
2.) n-1
3.) alpha level
4.) one tail is plus or minus, two tailed is ±
Assumptions for one sample t test
1.) The values in the sample must have independent observations
-Random sample scores have good external validity
2.)The population sample must be normal as the sample size grows
Conceptual Understanding of one sample t test
Subtract the mean of the sampling distribution (μ sub m) from the sample mean (M) and divide by the standard error (s sub m)
Sum of Squares
-SS
-Add all the (X-M)^2 together
Standard error
-S small m
-sum of squares/sqrt(n-1)
Cohen’s D
d= (M-μ)/s
sample mean-pop mean/sample SD
Cohen’s D Effect Size
0.2-small
0.5-medium
0.8-large
What do we calculate for a t test
The estimated standard error
95% Confidence interval equation [ ]
-Lower has a - sign
-(t value)(SE/S small m) + (mean)
When do you reject the null hypothesis
When the mean of the population doesn’t fall between the intervals (95% confidence interval)
Sample Standard Deviation
sqrt(SS total/n-1)
r^2 guidelines
0.01 or 1%-small
0.09 or 9%-medium
0.25 or 25%-large
