07 - 11 - 2014
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Parametric tests: Independent-samples t-test

Before comparison of independent groups (inhibition zones by species - see Example 1) we have to reset splitting conditions: after clicking the Split File button we should select Analyze all cases, do not create groups (as in the previous step, see Parametric tests: Paired (dependent) t-test, we splitted our data on groups).

The research question which will be solved by independent-samples t-test is: Are there differences between activity of oils against E. coli and E. faecalis?

This example we will illustrate together with discussing one of the possible errors which can appear during data analysis.

To specify the independent-samples t-test:

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

Independent-samples t-test

The Independent-Samples T Test dialog box opens:

Independent-samples t-test: definition of variables

2) Select the test variables (“TeaTree”, “TeaTreeGati”, “Thyme” and “ThymeGati”); click the upper transfer arrow button . The selected variables are moved to the Test Variable(s): list box.

3)  Select the grouping variable (“Species”); click the lower transfer arrow button . The selected variable is moved to the Grouping Variable(s): list box.

4) Now we have to define groups which we want to compare (E. coli and E. faecalis). Click the Define Groups… button. Define Groups dialog box opens.

5) Type E. coli and E. faecalis in the list boxes for Group 1: and Group 2:, respectively:

Independent-samples t-test: definition of groups

6) Click the Continue button. This returns you to the Independent-Samples T Test dialog box.

7) Click the OK button. An Output Viewer window opens.

Indication of error during analysis

In the Output Viewer window, instead of results with t-test statistics present warning which indicates that grouping variable is not applicable for the analysis and because of this the procedure was interrupted. To understand possible cause of errors we should open Variable View in the Data Editor. As we had chosen variable “Species” as grouping variable we should check its Measure and Width properties. A measure was selected as Nominal, this type is applicable for grouping variable, but width was specified as “10”, which appeared to be too long for grouping variable. Let us change width to “5”:

Typing different width of values of the “Species” variable

In the Data View window we can see then that names of species are shortened to five symbols:

Results of width change

Next we should repeat specifying the independent-sample t-test analysis but during defining groups such shortened values should be typed: “E.col” and “E.fae”:

Redefining of groups

After clicking the OK button, the Output Viewer window displays results with statistics.

The results of the independent-samples t-test analysis contain a table with group statistics (number of cases, mean, standard deviation and standard error of the mean) and a table with statistics for the t-test itself.

Statistics of groups

Independent-samples t-test: results

The Independent Samples Test table contains two groups of statistics – Levene’s test and t-test. The Levene’s test assesses equality of variances in compared groups. The null hypothesis assumes that variances are equal and when such condition is satisfied, it is a good result. In our example significance is more than 0.5 for all variables, so null hypothesis is not rejected. T-test is calculated then for both situation – with equal or non-equal variances, and we can choose t-test which is applicable for our situation. However, we can see that results for both situations are almost the same: for all studied variables differences between inhibition zones against E. coli and E. faecalis are statistically significant (p = 0.001 for tea tree oil, p = 0.002 for tea tree oil with gatifloxacin, p = 0.031 for thyme oil and p = 0.002 for thyme oil with gatifloxacin).

Knowing that differences between compared groups are statistically significant and looking to table with group statistics we can say which values are bigger: activity of tea tree oil either alone or with gatifloxacin was higher against E. coli (means for inhibition zones were 15.5 mm for tea tree oil alone and 17.0 mm for tea tree oil with gatifloxain against E. coli, while 11.2 mm and 12.9 mm, respectively, against E. faecalis). For thyme oil results were opposite – inhibition zones were bigger against E. faecalis.

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