Color Frequency Activity 9.4 Instructions
Color Frequency 1.......00 4..00 8...00 Activity 9.4 Instructions Document
Create an analysis using SPSS for a Chi-Square Goodness of Fit based on a real-world example involving M&M candies, including data import, hypothesis formulation, analysis execution, and reporting results according to APA guidelines.
Paper For Above instruction
The following paper details the process of conducting a Chi-Square Goodness of Fit test using SPSS, based on a scenario involving M&M candy color distribution analysis. The goal is to verify whether the observed frequencies of colors in a purchased bag match the expected frequencies provided by the manufacturer, using the statistical software SPSS for analysis, interpreting the results, and reporting them in APA format.
Introduction
The Chi-Square Goodness of Fit test is a non-parametric statistical procedure used to determine whether observed categorical data significantly differ from expected distributions. This test is particularly useful in assessing whether discrete data conform to theoretical distributions, such as the color proportions of M&M candies. The current analysis uses a real-world example where a graduate student research assistant (RA) wants to examine whether the proportion of M&M colors in a purchased bag aligns with the manufacturer's advertised distribution using SPSS.
Methodology
Data Collection and Setup
The RA procured a bag of M&Ms randomly from a local store, then sorted and counted the candies by color. The expected proportions, as published by the M&M company, are Blue (24%), Orange (20%), Green (16%), Yellow (14%), Red (13%), and Brown (13%). The observed counts were obtained through manual tally, and percentages were calculated based on the total candies in the sample. These data were imported into SPSS for analysis.
Importing Data into SPSS
Using the provided Excel spreadsheet “9.4 Data Input,” the RA imported the data into SPSS to create a dataset suitable for the Chi-Square analysis. This dataset included variables such as color categories and corresponding observed frequencies. The SPSS file was saved with the filename “9.4 SPSS MandM Chi Square Dataset.sav.”
Formulation of Hypotheses
The null hypothesis (H0) states that the observed color distribution matches the expected distribution: the proportions of colors in the bag are consistent with the manufacturer's claimed percentages. The alternative hypothesis (H1) posits that there is a significant difference between observed and expected distributions, indicating that the sample does not conform to the expected proportions.
Analysis Procedure
Using SPSS, a Chi-Square Goodness of Fit test was conducted. The test compared the observed frequencies with the expected frequencies calculated based on the total number of candies counted and the expected proportions. The output included the chi-square statistic, degrees of freedom, and p-value.
Results and Interpretation
The Chi-Square analysis yielded a chi-square statistic of X2 = [insert value], with df = [insert value], and a p-value of [insert value]. These results were formatted according to APA standards: "A chi-square goodness-of-fit test indicated that there was [significant/not significant] difference between observed and expected color distributions, χ2([df]) = [X2], p = [p-value]."
Interpretation of findings
If the p-value was less than the significance level (typically 0.05), the null hypothesis would be rejected, indicating that the observed distribution differs significantly from the expected distribution. Conversely, if the p-value exceeded 0.05, there is insufficient evidence to reject the null, suggesting the sample conforms to the expected proportions. Regardless of the outcome, the findings provide insights into how representative the sample is of the expected distribution.
Reporting and Write-up
The analysis and findings were documented in APA style, including a clear description of the variables, statistical test, results, and conclusions. The SPSS output was saved as “9.4 SPSS MandM Chi Square Output.spv” and included in the submission. The final write-up summarized all relevant variables, test statistics, and interpretations coherently, adhering to APA guidelines.
Conclusion
This exercise demonstrated the process of executing a Chi-Square Goodness of Fit test in SPSS, from data importation through hypothesis testing to results reporting. Findings from such analyses help validate whether observed categorical data align with theoretical expectations, which is fundamental in research across disciplines.
References
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