If An Experiment Is Conducted With 5 Conditions And 6 056918

If An Experiment Is Conducted With 5 Conditions And 6 Subjects In E

1. If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe? 2. The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table. 12-year-olds, 16-year-olds, 30-minute and minutes. Please use this link to answer problems 3 and 4. 3. (AT) The dataset ADHD Treatment has four scores per subject. a. Is the design between-subjects or within-subjects? b. Create an ANOVA summary table. 4. (AT) Using the Anger Expression Index from the Angry Moods study as the dependent variable, perform a 2x2 ANOVA with gender and sports participation as the two factors. Do athletes and non-athletes differ significantly in how much anger they express? Do the genders differ significantly in Anger Expression Index? Is the effect of sports participation significantly different for the two genders? 13.2 The F Distribution and the F-Ratio Use the following information to answer questions five and six. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are from various regions: Northeast, South, West, Central, East, with sample sizes and mean ages. 6. F degrees of freedom are involved: df(numerator) and the F statistic value. 7. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Examine results from a study shown in Table 13.24. 8. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics, and Asians? Data is from Table 13.26. 9. A survey on daily commuting mileage across different socioeconomic groups. 10. Variance comparison between spending on Saturdays and Sundays at the mall, based on results in Table 13.34. The document also includes detailed contractual and legal case information, which are not relevant for the statistical analysis requested.

Paper For Above instruction

The assignment involves understanding and calculating key statistical concepts such as degrees of freedom, analysis of variance (ANOVA), F-distribution, and related concepts using hypothetical data scenarios and real-world examples. Specifically, questions focus on experimental design measures (df and dfn), conducting ANOVA tests on datasets involving factors like age, gender, sports participation, and regional differences, and interpreting F-ratios to assess the equality of means across groups.

In the first question, the focus is on understanding the degrees of freedom in an experiment with five conditions and six subjects per condition. The numerator degrees of freedom (dfn) are typically calculated as the number of conditions minus one (k-1), which in this case is 4, and the denominator degrees of freedom (dfe) relate to the total number of subjects minus the number of groups, calculated as (k * n) - k, which is 30 - 5 = 25. This understanding is fundamental for conducting various ANOVA tests, as df determine the shape of the F-distribution that is used to evaluate statistical significance.

The second question involves analyzing data from a hypothetical study on reading comprehension, where age groups and time intervals are factors. Conducting a two-factor ANOVA requires calculating the sum of squares within and between groups, degrees of freedom, mean squares, and the F-ratios. The data provided with the age groups (12-year-olds, 16-year-olds, and 30 minutes vs. minutes) would be organized into a table to compute the ANOVA summary. This analysis helps determine if age and time significantly impact reading scores and if there is an interaction effect between these factors.

The third question asks whether the dataset ADHD Treatment, which contains four scores per subject, represents a between-subjects or within-subjects design. Based on the description, if each subject has multiple scores, this typically indicates a within-subjects design, as the same subjects are tested under different conditions or times. The subsequent task of creating an ANOVA summary table involves calculating the variance attributable to different sources such as subjects, conditions, and error, to statistically evaluate differences across the scores.

In question four, a 2x2 ANOVA involving gender and sports participation as factors is performed using the Anger Expression Index. The analysis explores main effects for gender and sports, as well as the interaction effect. The objective is to assess whether athletes and non-athletes significantly differ in anger expression, whether gender differences are significant, and if the effect of sports participation depends on gender. The ANOVA summary table will include sources of variance, sum of squares, degrees of freedom, mean squares, F-values, and significance levels.

Further, questions related to the F distribution and F-ratio involve interpreting empirical data such as regional differences in driver licensing age, average viewing times of news stations, and frequencies of eating out among different ethnic groups. Calculations of F-statistics and degrees of freedom in these contexts are critical for testing hypotheses about group equality. For example, using given sample means and variances, we compute F-ratios to determine whether observed differences are statistically significant or due to chance.

In a broader context, analysis of variances and F-tests are essential in experimental psychology, behavioral sciences, and social research for understanding the influence of multiple factors on a dependent variable. Proper interpretation of these tests aids researchers in drawing valid conclusions about the significance of observed differences among groups.

Overall, this assignment emphasizes applying statistical theory to practical data and experimental designs, understanding the computation and interpretation of degrees of freedom, and performing comprehensive ANOVA analyses to evaluate group differences. Proper handling of these statistical tools enables researchers to make informed decisions based on empirical evidence across diverse fields.

References

• Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). John Wiley & Sons.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
• Helsel, D. R., & Hirsch, R. M. (2002). Statistical Methods in Water Resources. U.S. Geological Survey.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Routledge.
• Levine, R. A., Krehbiel, T. H., & Berenson, M. L. (2000). Business Statistics: A First Course (2nd ed.). Pearson.
• Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
• Winer, B. J., Brown, D. R., & Michels, K. M. (1991). Statistical Principles in Experimental Design (3rd ed.). McGraw-Hill.
• Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson.
• McDonald, J. H. (2014). Handbook of Biological Statistics (3rd ed.). Sparky House Publishing.