TPC Journal V8, Issue 3- FULL ISSUE

268 The Professional Counselor | Volume 8, Issue 3 Math Placement Test–Algebra Subtest. The Math Placement Test is a university-made assessment designed to measure mathematic competence in algebra, trigonometry, and pre-calculus that helps the university place students in their first math course at the university. All first-time undergraduate students at the university are required to take the test; when data collection began, the mandatory completion policy was not yet in place, so some earlier participants had missing data in this area. The test is structured so that all respondents first take the algebra subtest and if they achieve 70% accuracy, they move to the trigonometry and pre-calculus subtests. Similar to the SAT, the researchers were unable to analyze psychometric properties of the test because the IKMO provided only composite and subtest total scores. Procedure Because the dependent variables (second-year retention and third-year retention) were dichotomous (i.e., retained or not retained), the researchers used the binary logistic regression procedure within SPSS Version 24 to analyze the data (Agresti, 2013; Hosmer et al., 2013; Tabachnick & Fidell, 2013). The purpose of binary logistic regression is to test predictors of the binary outcome by comparing the observed outcomes and the predicted outcomes first without any predictors and then with the chosen predictors (Hosmer et al., 2013). The researchers used a backward stepwise Wald approach, which enters all predictors into the model and removes the least significant predictors one by one until all of the remaining predictors fall within a specific p value range (Tabachnick & Fidell, 2013). The researchers chose to set the range as p ≤ .20 based on the recommendation of Hosmer et al. (2013). Preliminary data analysis included identifying both univariate and multivariate outliers, which were removed from the data file; conducting a missing data analysis; and testing the statistical assumptions for logistic regression. There were no missing values for categorical variables, but the assessment variables (CTI, SAT, and Math Placement Test) did have missing values. Results from Little’s (1988) MCAR test in SPSS showed that these data were not missing completely at random (Chi-square = 839.606, df = 161, p < .001). The researchers chose to impute missing values using the Expectation Maximization procedure in SPSS (Dempster, Laird, & Rubin, 1977; Little & Rubin, 2002). The data met the statistical assumptions of binary logistic regression related to multicollinearity and linearity in the logit (Tabachnick & Fidell, 2013). As previously discussed, the data also sufficiently met the assumption regarding the ratio of cases to predictor variables, with the exception of the ethnicity variable; after removing outliers, the Asian/Pacific Islander subcategory in the non-retained outcome had only four cases, violating the Peduzzi et al. (1996) and Field (2009) recommendation of having at least five cases. However, because the goal was to test the ethnicity categories separately rather than collapsing them to fit the recommendation, and because Hosmer et al. (2013) noted this was a recommendation and not a rule, the researchers chose to keep the existing categories, noting the potential limitation when interpreting this variable. Results The sections that follow provide the results from each of the hypotheses and interpretation of the findings. Hypothesis 1 Hypothesis 1 stated that the independent variables could predict undergraduate STEM retention from Year 1 to Year 2. As stated previously, the backward stepwise Wald approach involved including all predictors initially and then removing predictors one by one based on p value until all remaining