T test formula summary sheet - Peggy's website
[Pages:1]t test formula (1 sample)
standard error for 1 sample t test
t = M ? ? Sx
Sx = N
t-Test Formula Summary Sheet
One Sample t test
Sample mean (M) minus population mean you are comparing your sample to (?), divided by the standard error (Sx).
Sample standard deviation (, calculated with N-1 in the denominator) divided by the square root of the number of people (N).
degrees of freedom
df = N ? 1
Number of subjects (N) minus 1
t test formula (two samples)
t = M1 ? M2 Spooled
pooled standard error for Spooled = 2 sample t test
1 N1
2
+
2 N2
2
degrees of freedom
df = N ? 2
t test formula for r standard error of r
t = r ? Sr
Sr = 1 ? r2 N ? 2
Two Sample t test
Mean of group 1 (M1) minus mean of group 2 (M2), divided by the pooled standard error (Spooled). Standard deviation of group 1 (1) divided by the square root of the number of people in group 1 (N1), squared (2); plus standard deviation of group 2 (2) divided by the square root of the number of people in group 2 (N2), squared (2); then square root of everything ().
number of subjects (N) minus 2
t test of r vs. 0 correlation of interest (r) minus population correlation you are comparing to ( ? usually this is 0), divided by the standard error of r (Sr)
1 minus the squared r value, divided by N ? 2. Then take the square root of this.
degrees of freedom effect size (r)
df = N ? 2
r =
t 2
t2 + df
Number of subjects (N) minus 2
Effect size r (from t test) Using the t obtained from your t test, square the t value (t2) and divide by this squared t value plus the degrees of freedom from your t test (df). Then take the square root of this ().
? Margaret L. Kern, 2011
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