PSYC FPX 3700 Assessment 5 Categorical Data Analysis & ANOVA
Student Name Capella University PSYC-FPX3700 Statistics for Psychology Prof. Name Date PSYC FPX 3700 Assessment 5 Categorical Data Analysis & ANOVA PSYC FPX 3700 Assessment 5 focuses on applying statistical methods and interpreting psychological research. The assessment examines a chi-square test of independence using categorical student data, interprets a published study that uses one-way ANOVA, and evaluates the statistics-related requirements of a graduate psychology program. The chi-square analysis found no statistically significant association between admission type and program enrollment, χ²(2, N = 100) = 4.97, p = .084, while the reviewed research article found significant differences across sport types for several metacognitive measures. Part 1: Categorical Data Analysis The first part of PSYC FPX 3700 Assessment 5 uses the Assessment_5_Data.csv dataset. The hypothetical dataset represents undergraduate psychology students enrolled in a large academic program. Each observation corresponds to one student and includes an identification number, admission type, and academic program. The primary purpose of the analysis is to determine whether students’ admission status is associated with the psychology program in which they enroll. A chi-square test of independence is appropriate because both variables are categorical. Variables Included in the Dataset The dataset contains three primary variables: Conducting the Chi-Square Test of Independence A chi-square test of independence was conducted in JASP to determine whether admission type and program enrollment were statistically associated. This test evaluates whether the distribution of students among the three programs differs according to whether students entered as first-year or transfer students. The analysis also examined expected cell frequencies and calculated Cramér’s V. Expected frequencies help determine whether the assumptions of the chi-square test have been satisfied, while Cramér’s V provides an estimate of the strength of the relationship between the categorical variables. Assumptions of the Chi-Square Test Before interpreting a chi-square test, researchers should verify that the data meet the test’s assumptions. Two important considerations in this analysis were independence of observations and adequate expected cell frequencies. Independence of Observations Each student appears only once in the dataset and is classified into one admission category and one academic program. Therefore, each observation represents a separate student, satisfying the assumption that observations are independent. Expected Cell Frequencies The expected frequencies were also examined. All expected cell counts were at least 5, and none of the cells had an expected frequency of zero. Program First-Year Expected Count Transfer Expected Count Applied Behavior Analysis 10.15 18.85 General Psychology 14.35 26.65 Pre-Counseling 10.50 19.50 Because all expected frequencies meet the required threshold, the expected-count assumption for the chi-square analysis was satisfied. Statistical Significance of the Chi-Square Test The chi-square analysis was evaluated using an alpha level of .05. The results were: χ²(2, N = 100) = 4.97, p = .084. Because the p-value of .084 is greater than the .05 significance level, the result is not statistically significant. Therefore, the null hypothesis of independence cannot be rejected. In practical terms, the analysis does not provide sufficient statistical evidence to conclude that students’ admission type is related to their selected psychology program. Relationship Between Admission Type and Program Although the chi-square test was not statistically significant, the effect size was Cramér’s V = .223. Cramér’s V describes the strength of association between categorical variables, with larger values indicating stronger relationships. The observed effect suggests a modest association between admission type and program enrollment. However, because the chi-square test did not reach statistical significance, the finding should not be interpreted as evidence of a statistically reliable relationship in the population represented by the analysis. APA-Style Interpretation A chi-square test of independence was conducted to examine whether admission type was associated with program enrollment among 100 undergraduate psychology students. The analysis indicated that the association was not statistically significant, χ²(2, N = 100) = 4.97, p = .084, Cramér’s V = .223. Therefore, the distribution of students across Applied Behavior Analysis, General Psychology, and Pre-Counseling programs did not significantly differ according to whether students were first-year or transfer students. Part 2: Analysis of Variance The second part of the assessment involves interpreting a published psychological research article that used analysis of variance (ANOVA). The selected article is by Barrett et al. (2023), titled Sports Specific Metacognitions and Competitive State Anxiety in Athletes: A Comparison Between Different Sporting Types, published in Applied Cognitive Psychology. The researchers used ANOVA to investigate whether metacognitive beliefs and competitive anxiety differed among athletes participating in different types of sports. Descriptive Statistics in the Published Study The researchers reported means and standard deviations for the study’s outcome variables across four sport categories: For example, the MBPQ-PR (Metacognitive Belief in Personal Responsibility) subscale produced the following descriptive statistics: Sport Type Mean (M) Standard Deviation (SD) Endurance 2.76 0.92 Team 3.10 0.91 Individual 2.85 1.14 Esports 3.72 1.09 The mean represents the average score for each group, while the standard deviation describes the amount of variation in scores within that group. Descriptive statistics provide an initial picture of group differences before inferential statistical tests are interpreted. Type of ANOVA Used The researchers conducted one-way between-groups ANOVAs. The independent variable was sport type, which had four categories: endurance, team, individual, and esports. The dependent variables represented several dimensions of metacognitive beliefs, motivational processes, and competitive state anxiety. These included: The analysis did not include covariates or repeated-measures factors. Inferential Statistical Analysis One-way ANOVA is useful when researchers want to compare the means of three or more independent groups. In this study, the researchers used separate ANOVAs to determine whether athletes from different sport types differed on the measured psychological variables. When a statistically significant overall effect was identified, Bonferroni-adjusted post hoc comparisons were used to determine which specific groups differed from one another. The researchers also reported eta squared (η²) as an effect-size measure. Summary of the ANOVA Findings Several metacognitive and anxiety-related measures differed significantly according to sport type. For example, the MBPQ-PR measure produced a statistically significant result: F(3, N) = 5.76, p = .001, η² = .09. The results indicated that esports athletes had the highest scores on