The Relationship Between Being a Member and a Non-Member of an Athletic Team - Assignment Example

Data Analysis Project Executive Summary This report takes into account the correlation and association of variables presented indicating a survey in which a sample size of 261 participants were provided with questionnaires in order to respond on questions relating to gender, choice of exercises, relationship between being a member and a non-member of an athletic team and how such individuals find the SU facilities satisfying or not. The study assumes three different methods of data analysis. For the correlations, 2-sample t-tests were run to identify the relationship between being a member, a male/female, owning a car, or smoking and the intensity of exercise as well as the type of exercise. Additionally, the study applied a chi-square test to analyze the relationship between the ownership of a vehicle and the visiting of an outside facility besides the SU facilities. The results show that there are no relationships between gender & exercising once a week, and cigarette smoking & gender. Additionally, the results showed that there are substantial examples of associations between gender and the type of exercise, gender and the frequency of exercising, being a member or not of an athletic team and the rating as well as satisfaction of participants using the SU facilities. Major disparities in the results show that, although gender determines the type of exercise chosen, there are no major relationships between the frequency of attendance and the choice of attending exercise sessions once a week. Table of Contents Executive Summary 1 MEASUREMENT 2 Outline of questionnaire 2 AGGREGATE RESULTS 4 Frequencies 4 Means 5 Standard Deviation 5 ANALYSIS OF ADDITIONAL RESEARCH QUESTIONS 6 Cross-Tabulation of X1 and X12 6 Cross-Tabulation of X10 and X12 6 Cross-Tabulation of X1 with X11a 6 Cross Tabulation of X1 with X11b 7 Two-Sample T-Test and CI: X13, X1 7 Correlation: X1, X16A 7 Correlation: X1, X16B 8 Two-Sample T-Test and CI: X18A, X1 8 Two Sample T-Tests of Equality 8 Two-Sample T-Test and CI: X18B, X13 8 Equivalence Test: Mean(X21) / Mean(X13) 9 Two-Sample T-Tests of Equality 9 Equivalence Test: Mean(X22B) / Mean(X13) 10 Correlation: X14, X21 10 Chi-Square Test for Association: X7, X23 10 Works Cited 11 APPENDIX A: Minitab Output 11 MEASUREMENT Outline of questionnaire The measurement tool for this research is a questionnaire comprising of 6 questions for this section of the study which seeks to analyze the data on exercise habits and it relates one variable with another. The data set considered three types of question types comprising of multiple and closed-ended questions. For the multiple choice questions, the participants were expected to select any of the answers that suit them best. For the closed-ended questions, only answers such as ‘Yes’ and ‘No’ were allowed as this would make part of the numerical data analysis. Through the representation of results as ‘yes’ or ‘no’, numerically this can be presented logically as 1s and 0s for every ‘yes’ and ‘no’ respectively. In this case, questions that require ‘yes’ or ‘no’ answers provided the independent variables that other items on the variable list depended on. For instance, the questionnaire requires participants to indicate their sex. In this case, each male case is denoted as a 1 and every female participant is indicated as a 0. In this case, dependent variables such as the decision and choice to practice, the number of times individuals decided to practice, and the number of times any of participants has practiced once, twice, or more times in a week are tested. With reference to the presentation of the questionnaire structure, the questions are structured in three different ways that apply different analysis methods. The first set of questions are the closed-ended questions that either require a ‘yes’ or a ‘no’. These types of questions are applied in two major instances. Firstly, the questionnaire requires the participant to fill up/tick his/her gender so that in the analysis stage, the data can be analyzed from both male and female perspectives. On the other hand, the questions require the use of affirmative or negative answers. For participants that completed the survey, those who provided affirmative answers are represented by 1 and those that provide negative responses are represented by a 0. Through the simplification of the responses, statistical analysis is possible at this stage as the data is transformed into quantitative data. The second type of questions is comprised of those with multiple answers in which the activities and items require multiple answers such as the number of activities one is involved in. These questions require the individuals to outline the number of activities that they are involved in such as sports, exercises, and routinely activities. In the presentation of the data from the responses of the multi-answer questions, each response was coded numerically to indicate the item or variable tested. However, the multi-answer questions and the single-answer questions resembled each other except of the fact that the latter case only requires the choosing of a single option. These single-answer and multiple-answer questions would be coded as well such that they can be analyzed numerically like the other variables tested in the study. For questions with multiple choice responses regarding participant attitudes and perceptions, each response was graded and coded with respect to the weight placed on the response. For instance, participants were asked to rate various items with respect to their attitudes towards the items (SU facilities and their level of satisfaction). The numerical codes used would be applied in the analysis of the data as they represent the Likert-scale. In this case the Likert-scale method is represented with a Likert-7 scale in which the liking and dislike of a variable is weighted from 1 to 7. AGGREGATE RESULTS Frequencies The aggregate results involve the tabulation of statistical data from the provided data (exercisef03_fall2013.xls). The basic statistical functions include frequencies, means, and standard deviation of the data variables. However, while the data set has multiple variables occupying vast cells on the data analysis’s software worksheet, only the useful variables were selected in this case. Hence, the frequencies were identified as the number of times any numerical value occurs within a set of data. However, while using Minitab as the software for analysis, the frequencies of the data sets are presented with reference to the means. In this case, the frequency output shows the number of instances where the values are below and above the mean of the set. In this case, the selected variables include gender (X1), exercises every week (X12), smokes cigarettes (X10), type of exercise (X11a and X11b), equal number of times (X14), equal amount of time (X15), member (X13=1), non-member (X13=0), type of exercise (X16a and X16b), athletic teams (X18a and X18b), satisfaction level (X21), rating facilities (X22a and X22b), owner of vehicle (X7), and outside athletic facilities (X23). These variables were considered from the data set as they seek to provide an insight regarding the associations among various variables such as the use of athletic facilities and an individual owning a vehicle. In this case, it shows that all instances from Table 1 on Appendix A have higher number of items that exceed the mean. Additionally, the minimum and maximum columns show whether the produced results are within the ranges as higher or lower values than the maximum and the minimum values would indicate the presence of errors. Means On the other hand, the means of all the considered variables were tabulated. The variables considered in this case include gender (X1), exercises every week (X12), type of exercise (X11a and X11b), equal number of times (X14), equal amount of time (X15), member (X13=1), non-member (X13=0), type of exercise (X16a and X16b), athletic teams (X18a and X18b), satisfaction level (X21), and rating facilities (X22a and X22b). In this case, the means act like the threshold to dictate the frequencies of the data. Thus, results on the frequencies are determined based on whether the values are above or below the mean. Thus, for data presented as 1 or 0, any mean value below 0.5 shows that more negative responses and/or the female gender has the highest frequency. On the other hand, the number of mean variables showing a mean of 0.5 and above given the same conditions as above, show that more males participated while at the same time indicating that more affirmative responses were provided for the questionnaire questions. Standard Deviation The standard deviation for the data set indicates data for the same sample size as the means. In this case, the standard deviation of 5 out of the 11 variable sets is below the value of 1.0 while the rest have more than 2.0. Based on the data provided, the standard deviation of below 1.0 indicates the variables tested based on either affirmative answer or negative answer in which each is represented as 1 or 0 respectively. On the other hand, Table 1 in Appendix A shows the maximum and minimum values for the variables selected for standard deviation analysis. In this case, it shows that all the cases where 1 is a maximum value have a standard deviation less than 1.0 showing that the analysis is authentic and free or representation errors. ANALYSIS OF ADDITIONAL RESEARCH QUESTIONS Cross-Tabulation of X1 and X12 The cross-tabulation of X1 with X12 seeks to indicate the association between gender and whether the participant at hand exercises once a week. With a P-Value of 0.10 set as the determining factor of association, it is shown that there is no relation between gender and the choice of exercising once a week since the p-value in this case is 0.969 exceeding the determining factor of 0.1. Cross-Tabulation of X10 and X12 X10 and X12 represent data variables for cigarette smoking and whether an individual exercises once per week. In this case, the p-value is the determining factor as 1 above. The p-value of 0.1 would indicate the relationship between smoking and exercising. In this case, the result shows that a p-value of 0.414 results from the data set indicating no relationship between smoking and exercising Cross-Tabulation of X1 with X11a With reference to the type of exercise offered and the gender of the participant, the results for this tabulation provide 0.001 showing relationship between the gender and type of exercise. This shows that some exercises were designed for males or females alone. Cross Tabulation of X1 with X11b Additionally, the correlation of gender and type of exercise offered. In this case, as a p-value of 0.1, the result in this case show a p-value of 0.049 and 0.005 indicating strong relationship between the two variables. In this case, it is conclusive that the type of exercise offered at the SU divide students in gender terms such that some activities are within and outside the scope of females and/or males. Two-Sample T-Test and CI: X13, X1 Using the Two-Sample T-Tests for X13 and X1 indicates the equality the variables. The three variables considered in this case indicate being a member or not, exercises for the same duration, and number of times in a week. The correlation of the three variables show a p-value of 0.000 at a confidence level of 90%. This result shows a strong relationship among the variables tested. Correlation: X1, X16A Using the Two-Sample T-Tests for X16 and X1 indicates the equality of the variables. The two variables considered in this case indicate the gender and the exercise a student chooses. The correlation of the two variables show a p-value of 0.000 at a confidence level of 90%. This result shows a strong relationship among the variables. Correlation: X1, X16B Using the Two-Sample T-Tests for X16b and X1 indicates the equality of student gender and the exercise one picks. The two variables considered include gender and the type of exercise the student chooses. The correlation of the two variables show a p-value of 0.000 at a confidence level of 90%. This result shows a strong relationship among the variables. Two-Sample T-Test and CI: X18A, X1 Using the Two-Sample T-Tests for X18a and X1 indicates the equality of variables. The three variables considered in this case indicate being a member or not, exercises for the same duration, and number of times in a week. The correlation of the three variables show a p-value of 0.000 at a confidence level of 90%. This result shows a strong relationship among the variables tested. Two Sample T-Tests of Equality a. Two-Sample T-Test and CI: X18A, X13 Using the Two-Sample T-Tests for X18a and X13 indicates the equality of variables. The three variables considered in this case indicate being a member or not, reasons for exercising, and being a member of an athletic team or not. The correlation of the three variables shows a p-value of 0.000 at a confidence level of 90%. This result shows a strong relationship among the variables tested. Two-Sample T-Test and CI: X18B, X13 Using the Two-Sample T-Tests for X18b and X13 indicates the equality of the two variables. The three variables considered in this case indicate being a member or not, reasons for exercising, and being a member of an athletic team or not. The correlation of the three variables shows a p-value of 0.000 at a confidence level of 90% as the case with 7(a) above. This result shows a strong relationship among the variables tested (Boer, n.p). . Equivalence Test: Mean(X21) / Mean(X13) This tabulation seeks to identify whether the members and non-members of athletic teams are equally satisfied with the SU facilities. With a confidence level of 90% and a p-value of less than 0.1, an association between the two variables is established. The two-sample t-tests of equality of the means of X21 and X13 indicating the relationship between being a member and not being a member of an athletic team. In this case, the confidence level of 90 represents the upper limit and 10 the lower limit. The results show that there are not relationship between facility satisfaction for members and non-members of athletic teams. Two-Sample T-Tests of Equality b. Equivalence Test: Mean(X22A) / Mean(X13) This tabulation seeks to identify whether the members and non-members of athletic teams rate the features of SU facilities the same way. With a confidence level of 90% and a p-value of less than 0.1, an association between the two variables is established. The two-sample t-tests of equality of the means of X22A and X13 the relationships between how non-members and members of the athletic teams rate the features of SU facilities. In this case, a confidence level of 90% represents the upper limit and 10% the lower limit. The results show that there is a relationship between the ratings of a facility and the membership or non-membership of a participant. Equivalence Test: Mean(X22B) / Mean(X13) This tabulation seeks to identify whether the members and non-members of athletic teams rate the features of SU facilities the same way. With a confidence level of 90% and a p-value of less than 0.1, an association between the two variables is established. The two-sample t-tests of equality of the means of X22B and X13 the relationships between how non-members and members of the athletic teams rate the features of SU facilities. In this case, a confidence level of 0.9 represents the upper limit and 0.1 the lower limit. The results show that there is a relationship between the ratings of a facility and the membership or non-membership of a participant in athletic teams. Correlation: X14, X21 The Pearson correlation of X14 and X21 is 0.006 while the p-value of is 0.942. At a confidence level of 90% and a p-value of less than 0.1 as the qualifying factors of the association, it shows that there is no association given that the p-value exceeds 0.1 threshold. Chi-Square Test for Association: X7, X23 At a confidence level of 90% and p-value of less than 0.1, the chi-square output in this case shows no association between the ownership of a vehicle and the use of outdoor athletic facilities. The p-value in this case indicate p-value of 0.426 which is outside the range of 0.1 and below. Works Cited Boer, Keith. 2 Sample t-Test Using Minitab Release 17. Accessed online on December 15, 2014 from https://www.youtube.com/watch?v=OkffkyV3uNY APPENDIX A: Minitab Output Descriptive Statistics: X1, X12, X13, X14, X15, X16A, X16B, X18A, X18B, X22A, X22B Variable N N* Mean SE Mean TrMean StDev CoefVar Minimum Median Maximum Mode X1 261 0 0.4981 0.0310 0.4979 0.5010 100.58 0.0000 0.0000 1.0000 0 X12 255 6 0.7255 0.0280 0.7511 0.4471 61.63 0.0000 1.0000 1.0000 1 X13 200 61 0.1900 0.0278 0.1556 0.3933 206.99 0.0000 0.0000 1.0000 0 X14 196 65 2.4643 0.0676 2.4432 0.9467 38.41 1.0000 2.0000 5.0000 2 X15 188 73 64.87 1.90 64.03 26.04 40.15 10.00 60.00 150.00 60 X16A 185 76 0.2595 0.0323 0.2335 0.4395 169.40 0.0000 0.0000 1.0000 0 X16B 178 83 0.0843 0.0209 0.0375 0.2786 330.58 0.0000 0.0000 1.0000 0 X18A 196 65 5.153 0.120 5.284 1.682 32.63 1.000 6.000 7.000 6 X18B 196 65 5.7959 0.0912 5.9432 1.2767 22.03 1.0000 6.0000 7.0000 7 X22A 170 91 5.5118 0.0959 5.5921 1.2510 22.70 1.0000 6.0000 7.0000 6 X22B 173 88 4.827 0.110 4.890 1.452 30.09 1.000 5.000 7.000 4, 5 N for Variable Mode X1 131 X12 185 X13 162 X14 78 X15 69 X16A 137 X16B 163 X18A 57 X18B 67 X22A 61 X22B 44 Table 1: Aggregate Analysis 1. Correlation: X1, X12 Pearson correlation of X1 and X12 = 0.002 P-Value = 0.969 2. Correlation: X10, X12 Pearson correlation of X10 and X12 = -0.052 P-Value = 0.414 3. Correlation: X1, X11A, X11B X1 X11A X11A -0.361 0.001 X11B 0.222 -0.317 0.049 0.005 Cell Contents: Pearson correlation P-Value 4. Two-Sample T-Test and CI: X13, X14 Two-sample T for X13 vs X14 N Mean StDev SE Mean X13 200 0.190 0.393 0.028 X14 196 2.464 0.947 0.068 Difference = μ (X13) - μ (X14) Estimate for difference: -2.2743 90% CI for difference: (-2.3940, -2.1546) T-Test of difference = 0.1 (vs ≠): T-Value = -32.71 P-Value = 0.000 DF = 394 Both use Pooled StDev = 0.7223 5. Correlation: X1, X16A a. Pearson correlation of X1 and X16A = -0.447 P-Value = 0.000 b. Correlation: X1, X16B Pearson correlation of X1 and X16B = 0.290 P-Value = 0.000 6. Two-Sample T-Test and CI: X18A, X1 A. Two-sample T for X18A vs X1 N Mean StDev SE Mean X18A 196 5.15 1.68 0.12 X1 261 0.498 0.501 0.031 Difference = μ (X18A) - μ (X1) Estimate for difference: 4.655 90% CI for difference: (4.474, 4.836) T-Test of difference = 0.1 (vs ≠): T-Value = 41.40 P-Value = 0.000 DF = 455 Both use Pooled StDev = 1.1642 B. Two-Sample T-Test and CI: X18B, X1 Two-sample T for X18B vs X1 N Mean StDev SE Mean X18B 196 5.80 1.28 0.091 X1 261 0.498 0.501 0.031 Difference = μ (X18B) - μ (X1) Estimate for difference: 5.2978 90% CI for difference: (5.1549, 5.4408) T-Test of difference = 0.1 (vs ≠): T-Value = 59.93 P-Value = 0.000 DF = 455 Both use Pooled StDev = 0.9176 7. A. Two-Sample T-Test and CI: X18A, X13 Two-sample T for X18A vs X13 N Mean StDev SE Mean X18A 196 5.15 1.68 0.12 X13 200 0.190 0.393 0.028 Difference = μ (X18A) - μ (X13) Estimate for difference: 4.963 90% CI for difference: (4.762, 5.164) T-Test of difference = 0.1 (vs ≠): T-Value = 39.80 P-Value = 0.000 DF = 394 Both use Pooled StDev = 1.2156 B. Two-Sample T-Test and CI: X18B, X13 Two-sample T for X18B vs X13 N Mean StDev SE Mean X18B 196 5.80 1.28 0.091 X13 200 0.190 0.393 0.028 Difference = μ (X18B) - μ (X13) Estimate for difference: 5.6059 90% CI for difference: (5.4500, 5.7618) T-Test of difference = 0.1 (vs ≠): T-Value = 58.24 P-Value = 0.000 DF = 394 Both use Pooled StDev = 0.9406 8. Equivalence Test: Mean(X21) / Mean(X13) Output 1: Equivalent Test 9. a. Equivalence Test: Mean(X22A) / Mean(X13) b. Equivalence Test: Mean(X22B) / Mean(X13) 10. Correlation: X14, X21 Pearson correlation of X14 and X21 = 0.006 P-Value = 0.942 11. Chi-Square Test for Association: X7, X23 Rows: X7 Columns: X23 0 1 Missing All 0 58 8 22 66 56.17 9.83 1 102 20 49 122 103.83 18.17 Missing 1 0 1 * All 160 28 * 188 Cell Contents: Count Expected count Pearson Chi-Square = 0.617, DF = 1, P-Value = 0.432 Likelihood Ratio Chi-Square = 0.634, DF = 1, P-Value = 0.426 Read More