What is the appropriate inferential statistic to analyze Dr. Mendoza’s data?

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The question asks us to identify the appropriate inferential statistic to analyze Dr. Mendoza’s data, but we don’t have details about the data type, research design, or the comparison being made. Careful reasoning about what each statistic is used for will help illuminate which option could be appropriate in different scenarios.
Option: correlation coefficient r.
This statistic assesses the strength and direction of a linear relationship between two continuous variables. It is not used to compare groups or test a mean difference, but rather to quantify association. If Dr. Mendoza’s research aims to determine whether two quantitative measures move together, r would be relevant; it is not the right choice for comparing group means or for testing independence of categorical variables.
Option: t-test.
A t-test is used to compare the means of a continuous outcome between two groups. It comes in variants such as the independent samples t-test (two separate groups) or the paired t-test (same subjects measured twice). If the research question involves whether there is a difference in an outcome between two groups (or conditions) and the data meet assumptions (normality, scale of measurement, independent samples or paired design), a t-test could be appropriate. It is not applicable for more than two groups without modification, and it is not used to assess relationships between two continuous variables.
Option: ANOVA.
ANOVA, or analysis of variance, extends the idea of a t-test to more than two groups. It tests whether there are statistically significant differences among the means of three or more independent groups. If Dr. Mendoza’s study involves comparing outcomes across multiple categories or treatment groups, ANOVA would be the suitable choice, provided assumptions (normality, homogeneity of variances, independent observations) are reasonably met. Like the t-test, ANOVA does not assess associations between two continuous variables, nor does it directly test relationships between two metrics.
Option: chi-square.
Chi-square tests are used with categorical data. They assess whether observed frequencies in categories differ from expected frequencies under a null hypothesis, such as independence between two categorical variables (in a contingency table) or goodness-of-fit to a specified distribution. If the data are counts or frequencies in nominal or ordinal categories and the research question concerns patterns of categorical data rather than means or relationships between continuous measures, chi-square would be appropriate. It is not used for comparing means or for measuring linear relationships between continuous variables.
Option: z-score.
A z-score is a standardization of a data point relative to the population mean and standard deviation. It is not an inferential statistic by itself; rather, it is a descriptive or standardization tool that can be used within various inferential procedures (e.g., in constructing z-tests or standardizing data before analysis). By itself, a z-score does not answer a hypothesis test or comparison, so using z-score alone would not constitute the inferential statistic needed to analyze data across groups or relationships.
In summary, the appropriate choice depends entirely on the research questions and data structure: whether you are comparing means between two or more groups, examining relationships between continuous variables, or testing categorical associations. Each option has a specific domain of applicability, and selecting among them requires matching the data type (continuous vs. categorical), the number of groups, and the study design to the assumptions of the test.

PSC 041 001 SQ 2025 Optional Final Exam

What is the appropriate inferential statistic to analyze Dr. Mendoza’s data?

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