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07 - 11 - 2014
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## Parametric tests: One-sample t-test

Let us focus on the following example in order to illustrate application of the one-sample t-test. The study of Nzeako et al. (2006) demonstrated that diameter of inhibition zone around the disk with thyme extract was 10 mm against E. coli. Let us compare this result with our own study on thyme oil. So, research question is formulated as following: Do the results for diameters of inhibition zones around the disks with thyme oil in our study differ (see Example 1) from results for thyme extract from the study of Nzeako et al. (2006)? In other words we compare means from our study with another know mean (10 mm).

By this example we will illustrate:

1) Splitting of data with choosing one subset;

2) Application of the one-sample t-test.

There are several methods of selecting a subset of data for an analysis. One of them is illustrated below:

1) Click the Data menu and select Select cases… :

The Select cases dialog box opens:

2) In the Select section select the Based on time or case range option and click the Range… button. The Select case: range dialog box opens:

3) In the Select case: range dialog box type 1 in First case box and 12 in Last case box:

4) Click the Continue button. This returns you to the Select cases dialog box.

5) Click the OK button.

Now our statistical analysis will be performed only with the first 12 cases, which correspond E. coli. Note that excluded cases after selection are crossed.

To specify the one-sample t-test analysis:

1) Click the Analyze menu, point to Compare Means, and select One-Sample T Test… :

The One-Sample T Test dialog box opens:

2) Select the variable for the test (“Thyme”), click the transfer arrow button . The selected variable is moved to the Test Variable(s): list box.

3) Specify test variable (value with which we are going to compare our data – 10 mm): type 10 in the Test Value box.

4) Click the OK button. An Output Viewer window opens and displays the results of the one-sample t-test:

In the Output Viewer window two tables appear. The first table One-Sample Statistics contains descriptive statistics, such as number of cases, mean, standard deviation and standard error of the mean. The second table One-Sample Test contains results of this test itself; in this table first of all we have to look at the significance. In our example experimental data for thyme oil differ significantly from previously published for thyme extract. Significance value “0.000” is usually written as “p < 0.001”. Important information also present in the Mean Difference column: we see that, in average, our data are bigger than published on 4.9 mm.

After finishing this analysis we have to reset selection condition because for other tests we will use the whole dataset:

1) Click the Data menu and select Select cases…. The Select cases dialog box opens:

2) In Select section select the All cases option.

3) Click the OK button.