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Formulate the problem: What is it that you want to study? Why is it of interest? What is your hypothesis of what is going on? What are the possible benefits of the outcomes of the study? Why are you interested in the study?

Specify the variables to be measured (i.e., the responses): What things need to be measured to enable you to check out your hypotheses? Can they be measured? How will you measure them? Agree on the factors & levels to be used in the experiment: What characteristics do you want to study, either internal to the experimental units or external to them. (In the context of Math 160, what 2 groups do you want to study and what do they represent?)

Define the inference space for the experiment: To what population do you want your results to apply? Do you have to make any assumptions to make the inference?

Randomly select the experimental units: How will you sample from your 2 groups? Will you use random sampling or will you use some other method to select your experimental data, e.g., pseudo sampling schemes? Design the experiment: Generate the experimental design using appropriate methodology. What is the structure of the experiment? (In the context of Math 160, you need to determine if the groups are independent or if you will be using paired comparisons.)

Develop the math model & evaluate the design, redesigning if necessary: What differences are detectable by the experiment? Is this good enough? (In the context of Math 160, this step is not necessary. However, sample size calculations may be helpful for more advanced students.)

Collect the data: How did you collect the data? Were there any problems? If so, how did you handle the problems? Analyze the data: Apply the appropriate analysis method or methods. Formulate your conclusions: What does the data analysis tell you about your hypotheses? What recommendations would you make? Can you make any predictions regarding future observations? Validate your conclusions: Will you make any confirmation runs to support your conclusions? (In the context of Math 160, this does not apply)

Implement the results: Use the information you’ve collected to make the world a better place. FINAL PROJECT REQUIREMENTS You are to collect a quantitative response variable for samples from each of two groups. The groups can be different types of people (e.g., Males & Females, Stay-at-home Moms & Working Mothers, etc.), different types of things (large paper helicopters & small paper helicopters, etc.), different processes (studying with the TV on & studying at your desk in a quiet room).

You will then write a report and develop a short 5 min presentation. The report will contain the data, your hypotheses and data analysis. Other important information to be included is listed in "The Scientific Approach" handed out in class. At several points during the term we will discuss the Final Project using the Helicopter experiment as an example. Also I have available some past Final Reports that you will be able to look at to help you determine how you want to go about the write-up. I am not providing you with a specific template to follow. Final reports don't have to be typed. Good reports have the appropriate charts and graphs to help the reader see your approach and conclusions. Final presentations can be powerpoint presentations, posterboard displays, or overhead presentations. Content is more important than pizzazz. The goal is not to just stand up and talk. You should "present" something, namely the important highlights of your study. If your study involved groups of items, examples of them would be good to bring in.

Paper For Above instruction

The final project in this research involves a comprehensive investigation of a quantified response variable measured from two distinct groups. The goal is to formulate a clear research problem, establish hypotheses, and perform appropriate statistical analyses to draw meaningful conclusions about the differences or similarities between these groups. This process follows the scientific approach—starting from problem formulation to data collection, analysis, and interpretation—and aims to produce actionable insights that could improve understanding or guide future decisions.

Introduction

The essence of the study is to compare two groups based on a specific quantitative response variable. For example, this could involve comparing heights between males and females, testing performance of differently designed paper helicopters, or evaluating the effect of different studying environments on academic performance. The primary motivation is to understand whether the observed differences (or lack thereof) are statistically significant, thereby contributing to the existing body of knowledge within the context of the chosen research question.

Formulating the Research Problem and Hypotheses

Defining the research problem requires identifying the variables of interest and the groups to be compared. Once the problem is explicitly stated—such as comparing average test scores between two teaching methods or measuring the flight duration of different helicopter designs—the next step is to formulate hypotheses. Usually, the null hypothesis (H₀) posits no difference between the groups, while the alternative hypothesis (H₁) suggests a significant difference.

Variables and Measurement

The response variable should be specified precisely—such as height in centimeters, duration in seconds, or count data. Measurement tools and procedures should be consistent and reliable to ensure data validity. Additionally, factors influencing the response—like age, gender, or experimental conditions—must be identified and controlled as appropriate for the study design.

Experimental Design and Sampling

The selection of experimental units should be randomized to reduce bias, employing either true random sampling or a pseudo-random method if necessary. The experiment's structure depends on whether the groups are independent or paired. For example, comparing heights of different groups would involve independent samples, while measuring before-and-after effects on the same subjects would require paired samples. The design should specify levels of variables, including the conditions or treatments applied.

Data Collection and Analysis

Data collection procedures should be detailed, noting any issues encountered and how they were addressed. Once data are collected, appropriate statistical tests—such as t-tests (for independent or paired samples), analysis of variance (ANOVA), or tests for proportions—must be selected based on the data type and the experimental design.

For independent samples, if both groups are normally distributed with unknown and unequal variances, two-sample t-tests can be used with appropriate adjustments. For non-normal data or small sample sizes, alternative methods or data transformations may be necessary. For paired samples, a paired t-test is appropriate, analyzing differences within each pair.

Tests for proportions are suitable when the response is categorical, such as success/failure or presence/absence. Large sample sizes allow for z-tests, while smaller sizes may require other approaches. Confidence intervals should accompany hypothesis tests to provide an estimate of the magnitude and precision of observed differences or proportions.

Interpretation and Conclusions

The analysis results should be interpreted in the context of the hypotheses, considering p-values, confidence intervals, and effect sizes. Conclusions should address whether the null hypothesis can be rejected and the practical significance of the findings. Recommendations for future research or application should be made, along with considerations of the limitations and potential biases in the study.

Presentation of Results

The final report should include data visualizations such as charts and graphs to illustrate key findings clearly. The presentation should succinctly summarize the goals, methodology, results, and conclusions, highlighting the implications of the study. Examples, especially if the study involved multiple groups, should be included to provide concrete insights for the audience. The focus should be on conveying the scientific process and results effectively rather than on aesthetics alone.

References

• Agresti, A. (2018). Statistical Methods for the Social Sciences. Pearson.
• Dean, A., Voss, D., & Dwyer, C. (2013). Statistical Power and Sample Size. The University of Wisconsin.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Thinking. Brooks/Cole.
• Wright, B. D. (2012). Basic Statistics for the Behavioral Sciences. SAGE Publications.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. SAGE Publications.
• Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press.
• Laerd Statistics. (2020). Independent samples t-test in SPSS.
• Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statistics for the Behavioral Sciences. Houghton Mifflin.
• Zar, J. H. (2010). Biostatistical Analysis. Pearson Education.

Conclusion

This research methodology provides a structured framework for conducting rigorous comparative studies involving two groups. By carefully designing experiments, selecting appropriate statistical tests, and thoroughly analyzing data, researchers can draw meaningful conclusions that advance understanding in their field. Effective communication through detailed reporting and engaging presentation further enhances the impact of the findings, contributing to scientific knowledge and practical applications.

References

• Agresti, A. (2018). Statistical Methods for the Social Sciences. Pearson.
• Dean, A., Voss, D., & Dwyer, C. (2013). Statistical Power and Sample Size. The University of Wisconsin.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Thinking. Brooks/Cole.
• Wright, B. D. (2012). Basic Statistics for the Behavioral Sciences. SAGE Publications.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. SAGE Publications.
• Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. CRC Press.
• Laerd Statistics. (2020). Independent samples t-test in SPSS.
• Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statistics for the Behavioral Sciences. Houghton Mifflin.
• Zar, J. H. (2010). Biostatistical Analysis. Pearson Education.