Page 255 - Statistics for Dummies

Because μ is equal to 0 if H is true, it doesn’t really need to be included in the
o
d
formula for the test statistic. As a result, you sometimes see the test statistic
written like this:
For the reading scores example, you can use the preceding steps to see whether
the computer method is better in terms of teaching students to read.
To find the statistic, follow these steps:
1. Calculate the differences for each pair (they’re shown in column 4 of
Table 15-1).
Notice that the sign on each of the differences is important; it indicates
which method performed better for that particular pair.
2. Calculate the mean and standard deviation of the differences from
Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples 239
Step 1.
My calculations found the mean of the differences, , and the stan-
dard deviation is s = 4.64. Note that n = 10 here.
d d
3. The standard error is .
(Remember that here, n is the number of pairs, which is 10.)
d
4. Take the mean of the differences (Step 2) divided by the standard
error of 1.47 (Step 3) to get 1.36, the test statistic.
Is the result of Step 4 enough to say that the difference in reading scores
found in this experiment applies to the whole population in general? Because
the population standard deviation, σ, is unknown and you estimated it with
the sample standard deviation (s), you need to use the t-distribution rather
than the Z-distribution to find your p-value (see the section “Handling Small
Samples and Unknown Standard Deviations: The t-Test,” earlier in this chap-
ter). Using the t-table (in the appendix) you look up 1.36 on the t-distribution
with 10 – 1 = 9 degrees of freedom to calculate the p-value.
The p-value in this case is greater than 0.05 because 1.36 is smaller than (or to
the left of) the value of 1.38 on the table, and therefore its p-value is more than
0.10 (the p-value for the column heading corresponding to 1.38).
Because the p-value is greater than 0.05, you fail to reject H ; you don’t
o
have enough evidence that the mean difference in the scores between the
computer method and the phonics method is significantly greater than 0.

3/25/11 8:14 PM
22_9780470911082-ch15.indd 239
22_9780470911082-ch15.indd 239 3/25/11 8:14 PM