In addressing construct and criterion validity of the LUSSI questionnaire, the question asked was; how well did the Likert-items of the six tenets predict learners’ NOSI conceptions? Tables 4.1 provide data to address this question.
Table 4.1: LUSSI- Likert-type responses correlations (n = 90)
ASC1 ASC2 ASC3 ASC4 ASC5 ASC6 SC Total ASC1 Pearson Correlation 1 .177 .302** .113 .152 .092 .586**
Sig. (2-tailed) .098 .004 .295 .157 .392 .000 ASC2 Pearson Correlation .177 1 -.103 -.272* .069 .194 .290**
Sig. (2-tailed) .098 .340 .010 .523 .070 .006 ASC3 Pearson Correlation .302** -.103 1 .159 .154 .131 .526**
Sig. (2-tailed) .004 .340 .140 .152 .224 .000 ASC4 Pearson Correlation .113 -.272* .159 1 -.017 .056 .367**
Sig. (2-tailed) .295 .010 .140 .875 .605 .000 ASC5 Pearson Correlation .152 .069 .154 -.017 1 .289** .638**
Sig. (2-tailed) .157 .523 .152 .875 .006 .000 ASC6 Pearson Correlation .092 .194 .131 .056 .289** 1 .568**
Sig. (2-tailed) .392 .070 .224 .605 .006 .000 SC Total Pearson Correlation .586** .290** .526** .367** .638** .568** 1
Sig. (2-tailed) .000 .006 .000 .000 .000 .000 **. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed). SC = sum of construct based out of a possible 20
ASC = average of the construct with the highest value being 5.
Where; ASC1 = observations and inferences; ASC2 = change of scientific theories; ASC3 = scientific laws versus theories; ASC4 = social and cultural influence on science; ASC5 = imagination and creativity in scientific investigations; and ASC6 = methodology of scientific investigations.
154
Table 4.1 shows that five of the six variables correlate substantially (that is, r is between 0.367 and 0.586) with the dependent variable-SC Total. One of the variables, ASC2 ‘change of scientific theories’ has a correlation of 0.290 with SC Total which is not significant because it is less than 0.3. Tabachnick and Fidell (2001) suggest that a variable should have correlation between 0.3 and 0.7 for it to be significant; hence construct two ‘change of scientific theories’ was dropped when running Multiple Regression Normality plot analysis. In other words, the construct ‘change of scientific theories’ is an outlier hence was not considered for the data set on regression analysis as suggested by Tabachnick and Fidell (2001). Still from Table 4.1, no correlation is above 0.7 therefore five of the six variables were retained for the analysis. Collinearity diagnostics was performed on the five variables that had significant correlation with the dependent variable as part of the multiple regression procedure. This was done to pick up problems with multicollinearity that may not be evident in the correlation matrix. The results are presented in Table 4.2.
Table 4.2: Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. Collinearity Statistics
B Std. Error Beta Tolerance VIF
1 (Constant) 2.139 .510 4.195 .000 ASC1 1.206 .092 .378 13.159 .000 .892 1.121 ASC3 .858 .098 .254 8.762 .000 .875 1.142 ASC4 .779 .079 .272 9.848 .000 .965 1.036 ASC5 .994 .065 .443 15.405 .000 .890 1.124 ASC6 1.190 .095 .357 12.516 .000 .906 1.104
a. Dependent Variable: SC Total
Where; ASC1 = observations and inferences; ASC3 = scientific laws versus theories; ASC4 = social and cultural influence on science; ASC5 = imagination and creativity in scientific investigations; and ASC6 = methodology of scientific investigations.
From Table 4.2, two values are given, Tolerance and VIF [Variance inflation factor]. Tolerance is an indicator of how much of the variability of the specified independent variables in the model is not explained by the other independent variables in the model and is calculated using the formula 1-R2 for each variable. Pallant (2005) suggests that if the
155
value is very small (less than 0.10), it indicates that the multiple correlation with other variables is high, suggesting the possibility of multicollinearity. VIF is just the inverse of the tolerance value (1 divided by Tolerance). VIF values above 10 would be a concern here, indicating multicollinearity. As shown on Table 4.2, the tolerance value for each independent variable is between 0.875 and 0.906 which is way above 0.10; attesting that the multicollinearity assumption was not violated. This is also supported by VIF values, which are between 1,036 and 1.142 which are well below the cut-off of 10. These results are not surprising, given that Pearson’s correlation coefficient between these five independent variables with the dependent variable - SC Total was between 0.367 and 0.586 (see Table 4.1).
The variance in which learners’ conceptions of the NOSI could be explained by scores on the six NOSI tenets of the LUSSI was also used to further determine construct and criterion validity of the LUSSI questionnaire. Using Regression analysis, the two types of validity can be ascertained at the same time. The Model Summary box (Table 4.3) helps address variance issues regarding learners’ NOSI conceptions.
Table 4.3: Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
Dimension1 .969a .940 .936 .46402
a. Predictors: (Constant), ASC6, ASC4, ASC1, ASC5, ASC3 b. Dependent Variable: SC Total
Looking at the Model Summary box (Table 4.3), the given value under the heading R
Square is 0.940. This tells how much of the variance in the dependent variable (SC Total)
is explained by the model (including the five variables). Expressed as a percentage, it means the model (which includes the five variables) explains 94.0 per cent of the variance in SC Total. However, a sample of 88 can be considered not very big so the R square value in the sample tends to be rather an optimistic overestimation of the true value in the population hence the Adjusted R square statistics ‘corrects’ the value to a better estimate of
156
the true population value. In this case, this becomes 93.6 per cent. This is quite a respectable result when comparing to some of the results that are reported in literature.
Beta values under Standardized Coefficients (Table 4.2) help in determining which of the variables included in the analysis contributed to the prediction of the dependent variable. ‘Standardized’ means that values for each of the different variables were converted to the same scale for comparison. Construct ASC 5 ‘Imagination and creativity in Scientific Investigations’ had the largest beta value, 0,443. This meant that this variable makes the strongest unique contribution to explaining the dependent variable, when the variance explained by all other variables in the analysis is controlled for. The beta value for ASC 1 ‘Observations and inference’ was slightly lower indicating that it made a less contribution. All five variables made a significant unique contribution to the prediction of the dependent variable as suggested by Pallant (2005) because their Sig. values (see Table 4.2) are all less than 0.05. Actually they have the same Sig. value which is 0 meaning they are significant.
Assumptions like outliers, normality, linearity, homoscedasticity and independence of residuals were checked using two different ways. These are: inspecting the Normal Probability Plot of the regression standardized residuals and the residual scatterplot. These were requested as part of the analysis. Figures 4.1 and 4.2 illustrate how these assumptions were checked.
157
Figure 4.1: Normality P-P Plot of Regression Standardized Residual
In the Normal Probability plot, Figure 4.1 is evidence enough that the points do lie in a reasonably straight line from bottom left to right. This suggests there are no outliers and other assumptions like normality and linearity are not violated. Figure 4.2 below gives a scatterplot of the standardized residual analysis.
158
Figure 4.2: Scatterplot of the standardized residual analysis
In the Scatterplot of the standardized residuals (see, Figure 4.2), the residuals are roughly rectangularly distributed, with most scores concentrated in the centre (along the 0 point). There is no clear or systematic pattern to the residuals (e.g. curvilinear, or higher on one side than the other). Figure 4.2 shows that there are no deviations from a centralized rectangle suggesting that there is no violation of the assumptions. The presence of outliers can also be detected from the Scatterplot. Tabachnick and Fidell (2001) define outliers as cases that have a standardized residual (as displayed in Figure 4.2) of more than 3.3 or less than -3.3. From Figure 4.2, it is evident that there are no outliers and this suggests once again that there is no violation to the assumptions.