Statistics Essentials For Dummies (33 page)

If the
p
-value is less than
α
, reject H
_o
.

p
-values on the borderline (very close to
α
) are treated as marginal results.

Here's how you interpret your results if you use an alpha level of 0.05:

If the
p
-value is less than 0.01 (very small), the results are considered highly statistically significant — reject H
_o
.

If the
p
-value is between 0.05 and 0.01 (but not close to 0.05), the results are considered statistically significant — reject H
_o
.

If the
p
-value is close to 0.05, the results are considered marginally significant — decision could go either way.

If the
p
-value is greater than (but not close to) 0.05, the results are considered non-significant — don't reject H
_o
.

When you hear about a result that has been found to be statistically significant, ask for the
p
-value and make your own decision. Alpha levels and resulting decisions will vary from researcher to researcher.

General steps for a hypothesis test

Here's a boiled-down summary of the steps involved in doing a hypothesis test. (Particular formulas needed to find test statistics for any of the most common hypothesis tests are provided in the rest of this chapter.)

1. Set up the null and alternative hypotheses: Ho and Ha.

2. Take a random sample of individuals from the population and calculate the sample statistics (means and standard deviations).

3. Convert the sample statistic to a test statistic by changing it to a standard score (all formulas for test statistics are provided later in this chapter).

4. Find the
p
-value for your test statistic.

5. Examine your
p
-value and make your decision.

Testing One Population Mean

This test is used when the variable is numerical and only one population or group is being studied. For example, Dr. Phil says that the average time that working mothers spend talking to their children is 11 minutes per day. The variable, time, is numerical, and the population is all working mothers.

The null hypothesis in the Dr. Phil example is H
_o
:
μ
= 11 minutes. Note that
μ
represents the average number of minutes per day that all working mothers spend talking to their children, and the claim is that that mean is 11. The alternative hypothesis, H
_a
, is either:
μ
> 11,
μ
< 11, or
μ
≠
11. Let's suppose you suspect that the average time working mothers spend talking with their kids is more than 11 minutes, your alternative hypothesis would be H
_a
:
μ
> 11.

The formula for the test statistic for one population mean is

Z =
. To calculate it, do the following:

1. Calculate the sample mean,
, and the sample standard deviation,
s.
Let
n
represent the sample size.