discussion response

Marilyn Beazer BUSI 820 – Quantitative Research Methods June 2, 2026 Discussion Forum 3

D3.4.1.a Mean Visualization Test Score

The mean visualization test score is the average score earned by the participants on the visualization test. According to Output 4.1a, the mean score is calculated by adding all visualization scores and dividing by the total number of participants (Morgan et al., 2020).

D3.4.1.b Skewness Statistic for Math Achievement

The skewness statistic for the math achievement test indicates whether the distribution of scores is symmetrical or skewed. A positive skewness means scores are clustered toward the lower end with a few high scores, while a negative skewness means the opposite. This helps determine whether the data are normally distributed, which is important when selecting inferential statistical tests (Morgan et al., 2020).

D3.4.1.c Minimum Score for Mosaic Pattern Test

The minimum score for the mosaic pattern test may appear unusual because standardized tests can contain extreme low scores or coded values. This can happen due to participant error, missing data coding, or very low performance levels.

D3.4.2.a Variables with Skewness Above 1.00 or Below –1.00

Variables with skewness values greater than 1.00 or less than –1.00 are considered substantially skewed. These variables are not normally distributed and may require transformation or nonparametric statistical procedures.

D3.4.2.b Importance of the Answer

The answer is important because many inferential statistics assume normality. Severe skewness can affect the validity of statistical conclusions and increase the likelihood of inaccurate interpretations (Keller, 2018).

D3.4.2.c Agreement with Boxplot

Yes, the skewness findings should agree with the boxplot shown in Output 4.2. A skewed distribution will usually display uneven whiskers or extreme outliers on one side of the boxplot.

D3.4.3.a Participants with Missing Data

Output 4.2b identifies the number of participants who are missing data on one or more variables. Missing data occur when participants fail to answer questions or complete measures.

D3.4.3.b Percent with Valid Motivation or Competence Scores

The percentage of students with valid scores is determined by dividing the number of valid cases by the total sample size and multiplying by 100.

D3.4.3.c Missing Both Scores

No, Outputs 4.1 and 4.2b alone do not clearly indicate how many participants are missing both the motivation scale and competence scale scores simultaneously because the outputs summarize variables separately rather than jointly.

D3.4.4.a Interpretation of Means

The means describe the average performance or characteristic of the sample on the measured variables. Means allow researchers to compare groups and identify trends in the data.

D3.4.4.b Total Participants

The total number of participants is the complete sample included in the study.

D3.4.4.c Participants with Complete Data

Participants with complete data are those who answered all required variables without missing responses.

D3.4.4.d Percent in the Fast Track

The percentage in the fast track is found by dividing the number of fast-track participants by the total sample size.

D3.4.4.e Percent Taking Algebra I in High School

The percentage who took Algebra I in high school represents the proportion of students reporting that coursework.

D3.4.5.a Asian-American Percentage

The 9.6% refers to the percentage of the total sample identified as Asian-American.

D3.4.5.b Students with Visualization 2 Scores of 6

The percentage with visualization 2 scores of 6 is determined from the frequency distribution in Output 4.5.

D3.4.5.c Students with Scores of 6 or Less

The cumulative percentage indicates the proportion of students who scored 6 or below on the visualization measure.

Keller, G. (2018). Statistics for management and economics (11th ed.). Cengage Learning.

Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2020). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.