Paper Example: A Two-Way Statistical Influence

This study sought to achieve two objectives aimed at answering the two main research questions. First, the study sought to establish if there exists a difference in student knowledge of environmental engineering concepts between 5th-grade students receiving instruction using constructivist versus traditional methods in controlling for aptitude. Second, the research sought to investigate if the difference in student knowledge of environmental engineering concepts between students receiving instructions using constructivist versus traditional methods, if any, was consistent between males and females in controlling for aptitude. These two objectives are entirely characteristic of a two-way ANCOVA analysis. Fundamentally, these two objectives will seek to answer the research questions by determining if there exists a two-way statistical influence. This will, therefore, be the priority in conducting the two-way ANCOVA analysis in SPSS because its outcome determines if the first aim of the research is incomplete. Assuming that the analysis finds a significant two-way influence, it will show that gender and method of teaching have different effects on the post-test scores. Therefore, the data analysis outlined in this chapter will be based on these two research objectives and related research questions. The data analysis involves a two-way ANCOVA conducted in SPSS involving two independent variables, a dependent variable, and a covariate.

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

Order now

Presentation of Data

The sample was made up of a total of 125 participants, 52.8% of whom were male and 47.2% female. Other descriptive statistics were as follows:

• IV Group
• Traditional Methods: 62 participants, 49.5% of the total population
• Constructivist Methods: 63 participants, 50.4% of the total population
• DV: Post-test scores (total): Range 16-100 with mean of 81.840 and SD of 21.692
• Traditional Methods: Range 16-100 with mean of 82.61 and SD of 22.376
• Constructivist Methods: Range 16-100 with mean of 81.08 and SD of 21.149
• Covariate: Pre-test scores (total): Range 15-100 with mean of 69.34 and SD of 19.635.
• Traditional Methods: Range 15-94 with mean of 72.81 and SD of 15.483
• Constructivist Methods: Range 15-100 with mean of 65.92 and SD of 22.613
• The data were screened to test for missing cases, normality, and identifying outliers.

Missing Cases Test

There were no established missing cases. This is because the test indicated that the range and means of both teaching methods were similar for the dependent variable, post-test science scores, and the covariate, pre-test science scores. This, therefore, indicated that all the cases were included in the data set.

Normality Test

Linearity Testing: this test involved a visual inspection of the scatterplots with Loess lines. The test indicated that there existed a linear relationship between post-test science scores and teaching method for females in traditional and constructivist classes and males in constructivist classes. There was a moderately linear relationship between post-test science scores and traditional methods for males. Based on these findings, the results need to be interpreted with caution.

Testing For Homogeneity: this test indicated Homogeneity of regression slopes as determined by a comparison between the two-way ANCOVA model with and without interaction terms, F(3,117) = 1.257. p=.292.

Homoscedasticity: This test involved visual inspection of simple scatterplots of the studentized residuals plotted against the predicted values for each group. The inspection indicated that there was a violation of homoscedasticity. A log-linear transformation was performed on the dependent variable, post-test science scores, with no difference in the results. See Figures 1 and 2 below. Even though violations of homoscedasticity were determined, the faculty advisor decided to continue with the analysis. As such, results may not be valid and should be interpreted with extreme caution.

Homogeneity of Variance: There was homogeneity of variances, as assessed by Levene's test of homogeneity of variance (p= .721).

Testing for Unusual Points (Outliers, Leverage Points, and Influential Points): Five cases were identified as outliers in the data, as assessed by cases with studentized residuals greater than 3 standard deviations. However, as one of the usual treatments is to transform the dependent variable and this had already been performed, the decision was made by the faculty advisor to leave those cases in the data set and proceed with further testing. There were no leverage or influential points, as assessed by leverage values and Cook's distance, respectively. Studentized residuals were not normally distributed, as assessed by Shapiro-Wilk's test with three of the four interactions having significant values (p<0.005): Traditional Methods for Females, Traditional Methods for Males, and Constructivist Methods for Males. As two way ANCOVA is fairly robust to deviations from normality, and the typical correction of transforming the dependent variable has already been completed, the faculty advisor chose to proceed with the analysis. However, all results from the ANCOVA should be interpreted with extreme caution as a Type I error is likely. This means that it is likely that the two way ANCOVA would show that there is a significant difference for teaching methods of science, when in fact there is not.

Data Analysis

After the screening of the data was complete, an analysis followed. The screened data were analyzed using a two-way ANCOVA in SPSS. Two-way ANCOVA, also known as factorial ANCOVA, is used in determining the interaction effect between two independent variables and a dependent variable. According to Dagar & Yadav (2016), a two-way ANCOVA considers the influence of two or more independent variables on a dependent variable while eliminating the impact of the covariate factor. As such, ANCOVA first involves the regression of the independent variables or the covariate on the dependent variable. This is followed by an ANOVA of the unexplained variance in the regression model. For McCormick & Salcedo (2017), the ANCOVA tests whether the independent variables have an impact on the dependent variable when the influence of the covariate has been eliminated.

Therefore, the process of data analysis involved performing analysis of covariance ANCOVA for two independent variables and a covariate variable. The procedure involved using techniques of multiple regression in estimating the parameters of the model and computing the least-squares means. Besides, the procedure provided the standard error estimates for least squares means as well as their differences. This also includes a computation of the T-test for the difference between the group means that have been adjusted for the covariate. As such, a response versus covariate was established through group scatter plots as well as residual to check model assumptions, as shown in the screening section above.

Assumptions in ANCOVA

Two-way ANCOVA involves similar to the linear models. However, there are two additional considerations, including the independence of the covariate and treatment effect, and the homogeneity of the regression slopes. In the first consideration, the covariate is not supposed to be different across the groups in the analysis. In addition, in conducting an ANCOVA, the overall relationship between the dependent variable or outcome and the covariate is considered. The regression line is fit to the entire data set without regard to the group in which an individual belongs. In doing this, an assumption is made that the overall relationship holds for all the groups of participants. As such, if the dependent variable has a positive relationship with the covariate, then it is assumed that the positive relationship holds for all the other groups. However, if the correlation between the covariate and the dependent variable differs throughout the groups, then the general regression model is not accurate and does not represent all the groups. This assumption, according to McCormick & Salcedo (2017), is fundamental and is referred to as the homogeneity of regression slopes assumption.

This analysis seeks to understand if a two-way interaction effect exists after controlling for one or more continuous covariates. The independent variables, in this case, included gender and method of teaching, while the dependent variable was the post-test scores. The science pretest scores were the covariate. No statistically significant two-way interaction between gender and method of teaching on science post-test scores, controlling for ability as measured by science pretest scores were detected, F(1, 120) = .088, p= .767, partial i2= .001. Therefore, an analysis of simple main effects for a teaching method and gender was performed with statistical significance receiving a Bonferroni adjustment and being rejected because of p=.265 for teaching method and p=.984 for gender. Table 1 below records the means, adjusted means, standard deviations, and standard errors for science post-test scores for the four groups.

Summary of Results

This research sought to answer the following research questions:

• Is there a difference in student knowledge of environmental engineering concepts between 5th-grade students receiving instruction using constructivist versus traditional methods, controlling for aptitude?
• Is the difference in student knowledge of environmental engineering concepts between students receiving instruction using constructivist versus traditional methods, if any, consistent between males and females, controlling for aptitude?

The traditional method involved 62 participants, which was 49.5% of the total population, whereas the other 50.4% (63) included constructivist techniques. The post-test scores ranged from 16-100 with a mean of 81.840 and a standard deviation of 21.692. The results indicated that the traditional method group scored a mean of 82.61 and a standard deviation of 22.376 within the range 16-100. On the other hand, the constructivist methods group indicated a mean of 81.08 and a standard deviation of 21.149 within the range 16-100. Under the covariate, the pretest scores range 15-94 with a mean of 69.34 and a standard deviation of 19.635. For the traditional methods group, the mean was 72.81 and standard deviation 15.483 within the range 15-94.

On the other hand, the constructivist method indicated a mean of 65.92 and a standard deviation of 22.613 within the range 15-100. After data collection for the independent variables (gender and method of teaching) and the dependent variable (post-test scores), the data were analyzed using a two-way ANCOVA analysis run through SPSS software. The influence of the independent variables was tested on the dependent was tested using the 0.05 alpha significance level. Therefore, the analysis resulted in the following conclusions.

There was no statistically significant two-way interaction between gender and method of teaching on science post-test scores, controlling for ability as measured by science pretest scores detected, F (1, 120) = .088, p= .767, partial i2= .001.