Identify The Variables, State The Level Of Data For Each Var

Identify the variables, state the level of data for each variable,

Section 1 requires identifying variables, their levels of measurement, and selecting appropriate statistics for different research questions.

Question 1: Do responses to the question “Were you born in the US?” differ for two different age groups, under 25 and 25 plus?

Variables: nativity status (“Were you born in the US?”, categorical: Yes/No), age group (under 25; 25 plus, categorical: ordinal if age group categories are ordered, nominal if not). The key variable here is nativity, with the two groups being compared based on age group.

Question 2: Does the average number of cars sold weekly differ for female and male salespersons?

Variables: number of cars sold weekly (continuous ratio), gender (categorical: nominal, with categories male and female).

Question 3: Is there a difference in the mean of survey scores measuring parental help with homework for two siblings at a high school?

Variables: survey scores (interval/ratio), sibling identifier or pair (paired/related samples), gender or other identifiers (if relevant). The key variable is survey scores (dependent), and the pairing is between siblings (related samples).

Question 4: What are the characteristics of a group of parents who have students in a kindergarten class at a local school district?

Variables: characteristics such as parent age, income level, education level, ethnicity (all categorical: nominal or ordinal), possibly continuous variables like income or age.

Question 5: Does a relationship exist between performance on an AIDS knowledge pretest and a posttest?

Variables: pretest scores and posttest scores (interval/ratio); relationship assessed via correlation or regression analysis.

Paper For Above instruction

Introduction

Understanding the nature of variables and their levels of measurement is fundamental in designing and analyzing research studies. Selecting appropriate statistical methods depends greatly on whether variables are categorical, ordinal, or continuous. This paper discusses the identification of variables, their levels, and the suitable statistical techniques for five different research questions, followed by a specific analysis based on the ELS data, and concludes with a discussion of validity threats and sampling strategies relevant to educational research.

Section 1: Variable Analysis for Sample Research Questions

Question 1 investigates whether responses to a binary question about nativity differ between two age groups. The variables involved include nativity status, which is categorical and nominal, and age group, which can be considered ordinal if the age groups are ordered (under 25, 25 plus). Since the interest is in the difference of proportions across groups, a chi-square test of independence would be most appropriate. The variables are nominal, and the data are categorical.

Question 2 examines whether the mean number of cars sold weekly varies by gender. Here, the variable of interest, number of cars sold, is ratio level (continuous), and gender is nominal with categories male and female. Comparing means across two independent groups suggests the use of an independent samples t-test (if data are normally distributed), with the variables being ratio (dependent) and nominal (independent).

Question 3 evaluates whether the mean survey scores differ between two siblings. The survey scores are interval/ratio variables, and the data are paired because the sibling scores are related. A paired samples t-test would be suitable here, considering the scores are measured for the same individuals or related pairs.

Question 4 describes analyzing characteristics of parents with children in kindergarten. Variables include demographic data, which can be categorical (e.g., ethnicity, education level) or continuous (e.g., income, age). Descriptive analyses such as frequencies, percentages, means, and standard deviations would provide insights into the population characteristics.

Question 5 explores the relationship between pretest and posttest scores on AIDS knowledge. Both variables are continuous (interval/ratio), and correlation or regression analysis would be most appropriate to examine the degree and significance of their relationship.

Section 2: Data Analysis from ELS Data

Using the given data, the variables friends_academic and friends_social are constructed as sums of specified survey items. These composite variables are intended to measure different dimensions of students' social networks.

Question 6: Comparing Relationship Differences Between Racial Groups

For White and Hispanic students, the correlation between friends_academic and friends_social can be computed separately. Testing whether these correlations differ significantly involves using Fisher's z-transformation to compare correlation coefficients. Effect size is measured by the magnitude of the correlations themselves, with higher correlations indicating stronger relationships.

Question 7: Comparing Means for Asian and Hispanic Students

To determine if mean scores of friends_academic and friends_social differ significantly between Asian and Hispanic students, independent samples t-tests should be performed. Effect sizes, such as Cohen's d, should be reported to quantify the magnitude of the differences. An APA table will summarize means, standard deviations, t-values, degrees of freedom, p-values, and effect sizes.

Question 8: Relationship Between Employment and GPA by Gender

For both females and males, chi-square tests can assess the association between having a job during the school year and GPA category (GPA ≤ 3.00 or GPA above 3.00). Odds ratios will provide effect sizes, indicating the strength of association. Comparison of these relationships evaluates whether employment status impacts GPA differently across genders.

Question 9: Mean Response Differences

For females, comparing responses to BYS54B and F1S40B involves paired samples t-tests since the same respondents provide both responses. Effect sizes will illustrate the practical significance of any differences.

Question 10: Proportion Differences in Employment

A chi-square test compares the proportions of Asian and Black students who held jobs during the school year. Effect size is measured by Cramér’s V, indicating the strength of association.

Section 3: Treatment Data Analysis

Question 11 asks which statistical test—independent t-test or paired t-test—is more appropriate given the data. The choice depends on the study design: for comparing pre- and post-treatment scores within the same group, a paired t-test is most appropriate; for comparisons between distinct groups, an independent t-test is suitable.

Question 12 involves stating the null hypothesis (e.g., no difference in scores pre- and post-treatment) and a non-directional alternative (e.g., there is a difference in scores, but it is not specified in which direction).

Question 13 discusses the conclusions regarding the effectiveness of the treatment. Significant differences, particularly with p-values less than .05, suggest the treatment had a measurable impact on the outcomes.

Section 4: Sampling, Validity, and Statistical Concepts

Question 14 recommends stratified sampling with adequate sample size for each subgroup—Latino, African American, Asian, and White students—to ensure representation and allow for subgroup comparisons. A sample size determined through power analysis should be sufficiently large to detect meaningful differences, typically 100-200 per group depending on expected effect sizes.

Question 15 clarifies the difference between experimental pre-post designs (which include control groups and random assignment) and quasi-experimental designs (lacking randomization), with the choice depending on experimental control and ethical considerations.

Question 16 discusses threats to internal validity (e.g., selection bias) and external validity (e.g., generalizability to broader populations). Strategies to mitigate include random assignment and representative sampling.

Question 17 distinguishes parametric from non-parametric statistics, with examples: t-test (parametric) and Mann-Whitney U test (non-parametric). Parametric methods assume data normality, while non-parametric methods do not.

Question 18 interprets the concepts of sum of squares (total variation), variance (average squared deviation), and standard deviation (square root of variance) using the data set (12, 13, 27, 27, 13, 28). The calculations illustrate how these measures quantify data variability.

Conclusion

In educational and social science research, proper identification of variables, their levels, and suitable statistical tests are essential. Understanding the nuances of sampling, validity, and statistical assumptions enhances the quality and interpretability of findings, guiding evidence-based decision-making in educational policy and practice.

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