Statistics Essentials For Dummies by Deborah Rumsey Page B

-distribution, Table A-1 in the appendix) and finding the probability of being at that value or beyond it (in the same direction). This p -value measures how likely it was that you would have gotten your sample results if the null hypothesis were true. The farther out your test statistic is on the tails of the standard normal distribution, the smaller the p -value will be, and the more evidence you have against the null hypothesis being true.
To find the p -value for your test statistic:
1. Look up the location of your test statistic on the standard normal distribution (see Table A-1 in the appendix).
     
2. Find the percentage chance of being at or beyond that value in the same direction:
     
a. If H a contains a less-than alternative (left tail), find the probability from Table A-1 in the appendix that corresponds to your test statistic.
     
b. If H a contains a greater-than alternative (right tail), find the probability from Table A-1 in the appendix that corresponds to your test statistic, and then take 1 minus that. (You want the percentage to the right of your test statistic in this case, and percentiles give you the percentage to the left. See Chapter 2.)
     
3. Double this probability if (and only if) H a is the not-equal-to alternative.
     
This accounts for both the less-than and the greater-than possibilities.
     
4. Change the probability to a percentage by multiplying by 100 or moving the decimal point two places to the right.
     
Interpreting a p-value
To make a proper decision about whether or not to reject H o , you determine your cutoff probability for your p -value before doing a hypothesis test; this cutoff is called an alpha level ( α ). Typical values for α are 0.05 or 0.01. Here's how to interpret your results for any given alpha level:
If the p -value is greater than or equal to α , you fail to reject H o .
     
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