## Directional (one-tailed) Techniques

We wish to answer the same basic question that was asked with two-tailed testing:

"How likely are we to get this sample if the null hypothesis is true?"
but we test a directional null hypothesis, as stated below:

We have the same basic four steps of hypothesis testing:

1. State the Hypotheses:
• Null hypothesis: Alcohol consumption does not decrease birth weight. Their weight will not be less than 18 grams (i.e., it will be equal to or greater than 18 grams). In symbols:
• Alternative Hypothesis: Alcohol will decrease birth weight. The weight will be less than 18 grams. In symbols:
2. Define the decision method:
• (Classic Approach: Define Decision Criterion)

• Determine the standard error of the mean (standard deviation of the distribution of sample means) for samples of size 16. The standard error is calculated by the formula:

The value is 4/sqrt(16) = 1.

• To determine how unusual the mean of the sample we will get is, we will use the Z formula to calculate Z for our sample mean under the assumption that the null hypothesis is true. The Z formula is:

Note that the population mean is 18 under the null hypothesis, and the standard error is 1, as we just calculated. All we need to calculate Z is a sample mean.

When we get the data we will calculate Z and then look it up in the Z table to see how unusual the obtained sample's mean is, if the null hypothesis Ho is true, using a one-tailed probabililty.

3. Gather Data:
The two experimenters got these different sets of data:

Experiment 1 Experiment 2
Sample Mean = 13 Sample Mean = 16.5

4. Evaluate Null Hypothesis:
We calculate Z for each experiment, and then look up the P value for the obtained Z, and make a decision. Here's what happens for each experiment:
Experiment 1 Experiment 2
Sample Mean = 13
Z = (13-18)/1 = -5.0
p < .0000
Reject Ho
ViSta Applet
Sample Mean = 16.5
Z = (16.5-18)/1 = -1.5
p = .0670
Do Not Reject Ho
ViSta Applet

ViSta's Report for Univariate Analysis of Experiment 1 Data.

ViSta's Report for Univariate Analysis of Experiment 2 Data.