Lab 8 (1)

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Jan 9, 2024

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Name: Sophia Farias Friday T.A. name/Class time: DIST 301 Monday/Wednesday lecturer: Munson Lab 8: Matched Pairs and 2 Sample Comparison of Means T-tests NOTE: Screenshots (Windows: WinKey-Shift-S, Mac: Cmd-Shift-4) of SPSS graphs and tables are sometimes necessary to show full completion of the lab. Please paste any requested images into the appropriate places in your lab report and submit the completed report via Brightspace (under the "Lab" folder) by 11:50 pm Friday. Two points will be deducted for each SPSS requested image that is not included in the submitted lab document. Also, six points will be deducted for late submission, up to 24 hours. Dataset : This lab uses the dataset ( FitnessChildren ), 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. This dataset contains information collected from 150 subjects in Germany who participated in a study examining the associations among physical fitness, concentration, and health-related quality of life in primary school-age children. When you have multiple columns of data, sometimes it can be tricky to tell the difference between a Matched Pairs and a 2-Sample Comparison of Means problem. Here’s how you know: Matched pairs : You get 2 measurements on the same unit (for example, before and after measurements or left- hand vs. right hand for everyone) OR you have measurements on two sets of units, with each individual of one set being paired off (matched by some trait) with an individual of the other set. We will measure the difference between each pair, and calculate only ONE MEAN , the mean of these differences. 2-Sample Comparison of Means : You have 2 separate populations from which you get 2 independent samples, and you just measure each unit once (for example, men vs. women, or undergraduates vs. graduates), i.e. there are TWO MEANS and there is no valid reason to pair up the subjects. Open your lab dataset in SPSS. Below you will find a description of the variables used in this lab. HG_left: Left hand grip strength in kilograms HG_right: Right hand grip strength in kilograms Sex: Sex of subject (girl, boy) Check the dataset variables description on Brightspace if you would like more details on the variables.

This dataset contains information for 150 subjects. The study aims to examine the associations among physical fitness, concentration, and health-related quality of life in primary school-age children . We are interested in the following from this dataset: (a) For each subject, we have measurements of their left-hand grip strength in kilograms ( HG_left ) and right-hand grip strength in kilograms ( HG_right ). (b) For all the 150 subjects, the researchers record sex of each subject ( Sex ), and also measured their right-hand grip strength in kilograms ( HG_right). There are two types of questions we can pose based on the two sets of data described in (a) and (b). We want to know: (1) Whether the population mean of right-hand grip strength in kilograms ( HG_right) differs between boys and girls ( Sex ). (2) Whether the population mean of right-hand grip strength in kilograms ( HG_right ) is greater than the population mean of left-hand grip strength in kilograms ( HG_left) , or whether the mean difference between HG_right and HG_left is positive. The following lab will refer to these data ((a) and (b)) and questions ((1) and (2)). The lab begins below. ● PAGES 12-14 IN THE SPSS INSTRUCTION MANUAL WILL ONCE AGAIN BE OF CONSIDERABLE USE TO YOU. ● ROUND YOUR ANSWERS TO 3 DECIMAL PLACES. 1. (1 point) For which of the above questions would you use Matched Pairs to answer, (1) or (2)? Which dataset can be used to answer that question, (a) or (b)? How do you know? You would use matched pairs to answer question 2 because this question involves the same variable for both groups with only two treatment conditions (left- or right-hand grip strength). Data set (a) would be used to answer this question since it contains information on left- and right-hand grip strength of the subjects. 2. For the question selected as a Matched Pairs case, analyze the dataset in SPSS using the appropriate statistical method of inference. Use α = 0.05. Note: Make sure you include here two SPSS outputs: the Paired Samples Statistics and the Paired Samples Test used for the following inferential procedures.

a. (2 points) What are your hypotheses? (Define the order you are using for the difference between the variables (e.g. " variable 1 " - " variable 2 "). Variable 1 = HG_right Variable 2 = HG_left H 0 : μ 1 − μ 2 = 0 H A : μ 1 − μ 2 ≠ 0 b. (2 points) Answer all the questions below. (Notes: (i) running the matched pairs test in SPSS will give you all the relevant output; (ii) to make the table/output fit on a page in Word, right click in it, then click on “AutoFit to Contents”). What are the individual means for the two lists of data, round your answer to 4 decimal places ? μ 1 = 14.2397 μ 2 = 13.8448 What is the SAMPLE mean difference, round your answer to 3 decimal places ? μ 1 − μ 2 = 0.395 c. (1 point) What is the 95% confidence interval for the POPULATION mean difference ? Round your answer to 3 decimal places, otherwise only partial credit will be given. ( 0.039,0.750 ) d. (2 points) What are your (i) test statistic, (ii) probability statement for the test statistic and (iii) p-value corresponding to the hypothesis test in part (a) of question 2? (i) t = 2.194 (ii) P ( Z = 2.194 ) (iii) P = 0.030 ( 2 − Sided Test ) e. (2 points) What is your conclusion in terms of the story ? Use a 5% significance level . Make sure to specify whether your conclusion refers to the population or the sample . My conclusion in terms of the story is that we should reject the null hypothesis because the P-value of 0.030 for the population is less than 5% (0.05) meaning that there is a significant difference between the population and the sample. This means that the population mean of HG_right differs from that of the mean of HG_left. 3. (1 point) For which of the questions on the first page would you use a Two-Sample Comparison of Means to answer, (1) or (2)? Which dataset can be used to answer that question, (a) or (b)? How do you know? You would use a two-sample comparison of means to answer question 1 because you are looking at both right-hand grip strength and sex variables. To answer this question, you would use data set (b) because this data set has information on both sex and right-hand grip strength.

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4. Analyze the data from the two-sample comparison of means question in SPSS using the appropriate statistical method of inference. Do not assume equal variances. ( Notes: USE Sex as the “Grouping Variable” and define groups as “boy” and “girl”. Make sure you include here two SPSS outputs: the Group Statistics and the Independent Samples Test. The variable to analyze is HG_right). a. (2 points) What are your hypotheses? (Define the order you are using for the difference between the variables (e.g. " variable 1 " - " variable 2 "). Variable 1 “boy” Variable 2: “girl” H 0 : μ 1 = μ 2 H A : μ 1 ≠ μ 2 b. (2 points) Answer all the questions below. What are the individual means for the two lists of data? Round your answer to 4 decimal places. μ 1 = 14.9754 μ 2 = 13.5605 What is the difference in the means ? Round your answer to 3 decimal places. μ 1 − μ 2 = 1.415 c. (1 point) What is the 95% confidence interval for the difference of the means? Round your answer to 3 decimal places, otherwise only partial credit will be given. ( 0.328,2.502 ) d. (2 points) What are your (i) test statistic, (ii) probability statement for the test statistic and (iii) p-value corresponding to the hypothesis test in part (a) of question 4? (i) t = 2.573 (ii) P ( Z = 2.573 ) (iii) P = 0.011

e. (2 points) What is your conclusion in terms of the story ? Use a 5% significance level . Make sure to specify whether your conclusion refers to the population or the sample . My conclusion is that we should reject the null hypothesis because the P value of 0.011 for the population is greater than 5% (0.05). This means that the population mean of right-hand strength differs between boys and girls.

Lab 8 (1)

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