Lab 1-Sampling Methods and Bias Student

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Purdue University *

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Feb 20, 2024

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Name: Connor Wood TA name/office hour/email: Ziyi Wang/Friday 1:30 PM – 2:30 PM/ wang4538@purdue.edu Lecturer name: Christina Munson Lab 1: Sampling Methods/ Bias NOTE: SPSS outputs are necessary to show full completion of the lab. Please paste all SPSS outputs into your lab report and submit the completed reports including all requested tables and graphs via Brightspace (under the "Lab" folder) by 11:50 pm Friday. Two points will be deducted for each SPSS requested output that is not included in the submitted lab document. Also, 30% points will be deducted for late submission, up to 24 hours. Dataset : This lab uses the dataset ( SleepPatterns ), located on Brightspace under Lab in the Datasets submodule. Instructions for opening the dataset in SPSS are found as follows.  SPSS installed on a computer: Reference page 4 of the SPSS Instruction Manual  SPSS running remotely: Reference the slide “Opening your Dataset Remotely in SPSS via Go Remote” in the document “SPSS using Citrix access guidelines” on Brightspace. Two hundred fifty college students in Indiana participated in a study examining the associations among sleep habits, sleep quality and physical/emotional factors. Participants completed an online survey about sleep habits that included the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Horne-Ostberg Morningness Eveningness Scale (MES), the Subjective Units of Distress Scale (SUDS), and questions about academic performance and physical health. 1. (2 points) Form a simple random sample (SRS) of 5 subjects from the dataset with SPSS using page 6 of the SPSS Instruction Manual . Once the sample is formed, record the Height for each selected subject in table SRS #1 below. Next, compute the sample mean for the Height in one of the two ways below and record the calculated sample mean in the corresponding entry of Table 1. 1) C alculator: Add the five numbers and then divide by 5. 2) SPSS: Reference the SPSS Instruction Manual page 10 – Descriptive Statistics: Calculate the Mean . Make sure to move the variable Height to the variable box . SRS #1 1 2 3 4 5 BMI 66.93 71.67 62.64 71.29 67.68

2. (6 points) Repeat the processes in question #1 for three more SRSs. Note: There is no need to re-open the dataset each time. Simply repeat the sampling process from the previous question to obtain a new random sample. SRS #2 1 2 3 4 5 BMI 66.28 72.46 67.72 68.95 55.07 SRS #3 1 2 3 4 5 BMI 70.24 72.70 67.73 76.17 68.18 SRS #4 1 2 3 4 5 BMI 62.83 63.71 70.25 65.93 62.15 Fill in the table below with the mean values calculated for each sample: Table 1 : Height SRSs Means SRS #1 SRS #2 SRS #3 SRS #4 x i 68.0420 66.0960 71.0040 64.9740 Do the following before proceeding with the lab. Navigate to “Data -> Select Cases”, select “All Cases”, and click OK. This should bring back the original dataset. Pause for a moment and reflect on the following statements. This will help you understand what you have done and prepare you for the rest of the lab. Consider the sample means in Table 1. Are they all the same? Most likely not, because sample statistics such as the sample mean vary between samples. Furthermore, a small sample size, like those above, means that it is more likely that the chosen individuals are different from sample to sample, leading to much variability. The fact that variability is reduced by increasing the sample’s size is a concept used all semester. In general, the value of a population’s parameter is not known because the information needed to find it cannot be measured for every individual in the population. However, the parameter could be directly found if all the needed information was known. Continue with the lab. In questions 3 and 4 , consider the dataset of 250 subjects as if it were a fictitious “population” of interest.

3. (2 points) Using SPSS, calculate the mean Height for this fictitious “population”. Write the value below to 3 decimals and include the output from SPSS . Reference the SPSS Instruction Manual page 10 (mean) and 5 (copying output). Mean: 67.212 Descriptive Statistics N Minimum Maximum Mean Std. Deviation Height 250 55.07 76.23 67.2117 4.37872 Valid N (listwise) 250 4. a) (1 point) In your opinion, are the sample means in Table 1 similar to or different than the mean of the fictitious “population”? Was variability due to small sample size apparent? The sample means in Table 1 are different from the fictitious “population” because the sample size used was so small and had varying heights. b) (1 point) Explain how increasing the sample size would affect how the sample means compare to the mean of the fictitious “population”. Increasing the sample would affect how the sample means compare because there would be more data to compare. For the remainder of the lab , consider the dataset as a sample of the real population of interest. 5. (1 point) The subjects in the dataset answered a call for volunteers to participate in this study. Assuming every subject who volunteered has a recorded response for every variable, describe the bias that could possibly result from this sampling design . There is volunteer bias because the subjects were given a choice to participate in the study. 6. (2 points) What is an alternative sampling design that could avoid the bias mentioned in question #5? Explain how it would address the bias. You could do a stratified random sample and separate the subjects by gender and measure each subject when they are selected for that sample. 7. (1 point) The variables GPA and Height were measured through self-reporting . Describe the bias that could possibly result. Response bias could result because people could overestimate their height or GPA to make themselves look better.

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8. (2 points) How could you avoid the type of bias mentioned in question #7? Give at least one idea for each variable. For height, you could measure the subjects to verify they gave their correct height. For GPA you could have the subjects bring a transcript to verify their GPA. 9. a) (1 point) Consider the following scenario: Subjects were asked to volunteer for this study and were told they would be paid for their time spent completing a questionnaire. As part of the questionnaire, the subjects provided their own average hours slept per night. Also, some of the questions on the questionnaire asked personal questions that several subjects refused to answer. Given this information, do you think that the data from the questionnaire will provide an accurate reflection of all subjects’ average hours slept per night? No. b) (1 point) If so, explain why. If not, identify at least two flaws in the sampling method of the study. There is response bias because the subjects could easily lie about their average hours of sleep.