Results

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We used a two-factor ANOVA for each of the independent variables to determine statistical significance. Each ANOVA included one of the independent variables as an explanatory factor to examine the influence of each dependent variable. A comparison of the scores of the ETS developed pre-test and post-test indicates a significant difference exists in the improvement of the "Logical Reasoning" skills of the treatment group of subjects, but not the control group. Logical reasoning, as measured by the Diagramming Relationships test (p < .004, F = 7.75, df = 39, one-tailed) significantly increased for the treatment group. This important result indicates a substantial and measurable increase in logical reasoning skill occurred in the treatment group during the six-week period between tests. This finding allows rejection of the primary null hypothesis and provides support for the alternative that logical reasoning skill increased for the treatment group after six weeks of formalized spreadsheet training.

While the other three cognitive skills in Figure 1, namely spatial visualization, mnemonic skill, and sequencing ability were not significantly influenced by spreadsheet training, we found the greater the increase in a student's logical reasoning score, the lower the error rate in the spreadsheet that he or she developed (p < .000, F = 4.015). These empirical results are consistent with the explanation that there exists a significant positive association between increases in an end user's logical reasoning score and his or her ability to develop effective spreadsheets. The results of all pre- and post-tests are tabulated in Table 3 and graphically illustrated in Figure 2.

Table 3: Summary of Statistical Analysis of Test Scores (Means, standard deviations, and significance levels for the tests)

		Control (N=21)			Treatment (N=21)
		Pre-test	Post-test	p-value	Pre-test	Post-test	p-value
Tests:
Diagramming	Mean	9.05	10.16	0.860	8.05	10.87	0.004
Relationships	SD	3.21	3.28		3.29	3.28
Choosing a Path	Mean	6.00	5.04	0.860	5.14	4.86	0.630
	SD	2.88	2.69		2.78	2.74
Necessary	Mean	8.76	9.08	0.350	8.61	9.08	0.250
Arithmetic	SD	2.12	3.06		2.60	1.85
Operations
Nonsense	Mean	7.40	8.47	0.920	7.04	7.40	0.330
Syllogisms	SD	2.02	2.80		2.51	2.80

Figure 2: Comparison of Treatment Groups Scores

These results are important because it provides preliminary evidence that a significant change occurs in one cognitive skill (logical reasoning ability) during the spreadsheet training process. The results also identify one cognitive change that influences error rates in spreadsheet models. Further research should explore other cognitive changes that occur during spreadsheet training and focus on cognitive skills that help minimize errors in spreadsheet models.

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