Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

116 CHAPTER 4 | Variability
The n 2 1 degrees of freedom for a sample is the same n 2 1 that is used in the formulas
for sample variance and standard deviation. Remember that variance is defined as the mean
squared deviation. As always, this mean is computed by finding the sum and dividing by
the number of scores:
mean 5
sum
number
To calculate sample variance (mean squared deviation), we find the sum of the squared
deviations (SS) and divide by the number of scores that are free to vary. This number is
n 2 1 5 df. Thus, the formula for sample variance is
s 2 5
sum of squared deviations
number of scores free to vary 5 SS
df 5 SS
n 2 1
Later in this book, we use the concept of degrees of freedom in other situations. For
now, remember that knowing the sample mean places a restriction on sample variability.
Only n 2 1 of the scores are free to vary; df 5 n 2 1.
LEARNING CHECK
1. If sample variance is computed by dividing by n, instead of n 2 1, how will the
obtained values be related to the corresponding population variance.
a. They will consistently underestimate the population variance.
b. They will consistently overestimate the population variance.
c. The average value will be exactly equal to the population variance.
d. The average value will be close to, but not exactly equal to, the population
variance.
2. What is the value of SS, the sum of the squared deviations, for the following
sample? Scores: 1, 4, 0, 1
a. 36
b. 18
c. 9
d. 3
3. What is the variance for the following sample of n 5 4 scores? Scores; 2, 5, 1, 2
a. 34/3 5 11.33
b. 9/4 5 2.25
c. 9/3 5 3
d. Ï3 5 173
ANSWERS
1. A, 2. C, 3. C