Driv e accu racy. Green s in regul ation

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1 LEARNING ACTIVITIES FOR PART II COMPILED Statistical and Measurement Concepts We are providing a database from selected characteristics of golfers on the PGA Tour. Data are for 3 of the players, based on their end-of-year (2) information. The players are in three groups according to money won: group (players -), group 2 (players 2-3), and group 3 (players 4 to 5) (see table A, or the Excel file named PGA datasheet for the full data set). The variables listed by column in the database are player name, money won ($), world rank, average score, drive distance, drive accuracy, greens hit in regulation (%), putts per round, scrambling, sand saves (%), group membership (, 2, or 3 as listed previously), and whether the golfer is from the United States or another country. Table A Data on PGA Players Ordered by Money Won ( to, 2 to 3, 4 to 5) Name Money won Wo rld ran k Aver age scor e Driv e dista nce Driv e accu racy Green s in regul ation Pu tts pe r ro un d Scram bling Sa nd sa ve s Grou ping by mon ey U.S. vs. interna tional Singh Micke lson Garcia Perry From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

2 Kim Villeg as Harrin gton Cink Leona rd Allenb y Els Petter sson Apple From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

3 by Strick er Camp bell Weekl ey Traha n Ames Duke Hart Thom pson D Johns From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

4 on Perez Mayfa ir Clark Bryan t Pampl ing Love Badde ley Kelly Chapter 6 From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

5 Becoming Acquainted With Statistical Concepts We provide a database from selected characteristics of golfers on the PGA Tour. Data are for 3 of the players, based on their end-of-year (2) information. The players are in three groups according to money won: group (players to ), group 2 (players 2 to 3), and group 3 (players 4 to 5). The variables listed by column in the database are player name, money won ($), world rank, average score, driving distance, driving accuracy (%), greens hit in regulation (%), putts per round, scrambling, sand saves (%), group membership by money earned (, 2, or 3 as listed previously), and whether they are from the United States or another country. You ll find the database in Handout, Activity 2. (The database is also available as an Excel file named PGA datasheet. ) The first thing to do with every data set is evaluate the characteristics of the data set. In the following exercise we have used SPSS 22. to evaluate whether the data appear normal for scoring average. In SPSS we do the following: Use the pull-down menu for Analyze. Select the Descriptive Statistics bar. Select the Explore bar. You can now add average score to the Dependent List. Click on Statistics and check Descriptives with a 95% confidence interval and click Continue. Click OK to run the statistics. You can see from table 6. and figure 6. (and from the SPSS results) that the data are reasonably normal in distribution. The mean (7.) and standard deviation (.54) for scoring average are also depicted in table 6.. Note, however, that the standard deviation is very small relative to the mean, because the range of scores is small (69.2 to 7.22). Skewness is slightly positive and kurtosis is slightly negative but are within normal expectations. Table 6. Descriptives Statistic Standard error Scoring Mean From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

6 average 95% confidence interval for mean Lower bound 69.2 Upper bound % trimmed mean Median 7.6 Variance.29 Standard deviation Minimum 69.2 Maximum 7.22 Range 2. Interquartile range.66 Skewness Kurtosis The normality of the data is further confirmed by looking at the histogram (with normal curve overlaid) shown in figure 6.. We got this figure in SPSS the following way: Use the pull-down menu for Analyze. Select the Descriptive Statistics bar. Select the Frequencies bar. Select average score for Variable(s). From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

7 Click the chart option and select Histograms with Show Normal Curve on Histogram checked. Click Continue and then click OK to get the chart. Figure 6. Histogram with overlay of normal curve for scoring averages. We suggest that you do this exercise with the students in your research methods class. We have found it effective to do this as a group if you have the facilities to do so. We reserve our computer lab where each machine has SPSS loaded. We then give each student the entire data set (Handout, Activity 2 or the Excel file named PGA datasheet ) as an SPSS file. This can be done using a thumb drive or, more efficiently, as an attachment. We bring a laptop with SPSS and the data loaded on it and use an LCD projector and From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

8 screen to show each step in the process. We do this on the laptop, and students (working alone or they can work in pairs if there are not enough computers) do it on their own machines and print a hard copy for annotation. We point out each of the features so they can annotate on the hard copy. If you don t have the resources to do this in a group, you can go over the process in class using a laptop and LCD projector, and then send each student a PDF of the results to complete the assignment outside of class. Chapter 7 Statistical Issues in Research Planning and Evaluation Review the information from activity 2 in chapter 6. One of the most important statistical skills is to estimate power (chances of rejecting a false null hypothesis) when reading or planning studies. We can use our database on PGA golfers to demonstrate this process. Suppose you would like to do a study on college golf teams in 29 to evaluate if they differ from the top PGA players in saves of par from the sand trap (the variable sand saves in the Excel file named PGA datasheet ). From the data, you could calculate the data on the PGA top players; in 2 they saved par 5.% of the time from the sand trap (SD = 5.%). You would like to know if the 29 college golf players in the Southeastern conference differ significantly from that percentage of par saves from the sand. You know the average percent of sand saves among SEC college golfers in 2 was 4% (SD = 6.%). How many SEC and PGA players from 2 would you need sand save data on to produce a significant difference (p =.5) with a power of.? To do this analysis, do the following: Go to the Power Calculator at Bullet Calculate Sample Size (for specified Power). Enter the value of the first mean, PGA players, 5.. Enter the value for the second mean, SEC golfers, 4. Enter sigma, a common standard deviation, by entering the 2 SD for the SEC golfers, 6. (that is the most conservative estimate since it is larger). Select a -Sided Test since you are interested in whether the SEC golfers have lower values than the PGA players. Confirm that alpha is set at.5 and power at.. Click Calculate to get the needed size per group. The program will then calculate that the sample size needed from the 2 PGA and SEC golfers is 32 players for each group. Thus, if the differences between the SEC and PGA golfers in saving par from sand From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

9 traps in 29 is about as it was in 2, you will need to collect data on about 32 players from each group. It s always safe to be conservative here, as we have been, by using the larger standard deviation, and it might be wise to collect data on about 35 in each group. Chapter Relationships Among Variables First, it might be useful to have students see a graphic display of a high and low relationship between two variables. To do this in SPSS, do the following: Click on the Analyze pull-down menu. Select the Regression bar. Select the Curve Estimation bar. Enter money won as the dependent variable (y axis) and average score as the independent (x axis). Make sure Linear is checked in the model box. Click OK to get the figure. You will now see what we show in figure.. The relationship is a strong one (only the leading money winner, V.J. Singh, is very far off the regression line). Also note that the relationship is negative: More money won is associated with a lower average score. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

10 Figure. High but negative relationship between scoring average and money earned on PGA Tour. To demonstrate a positive relationship, go through the same process, but substitute world rank and average score for the dependent and independent variables. Figure.2 shows this positive relationship. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

11 Figure.2 Strong positive relationship between average score and world rank. Do the following to demonstrate the correlations between each pair of the variables in the data set: Click on the Analyze pull-down menu. Click on the Correlate bar. Click on the Bivariate bar. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

12 Enter the nine continuous variables (all but Grouping by money and U.S. vs. international. ) Click on OK to get the correlation matrix. You will see output that is similar to table., where there is a relationship, r, between each pair of the variables (e.g., money won vs. average score, money won vs. driving distance). There are several that have strong relationships, some positive and some negative:.7 between money won and average score. That is, lower scoring averages are associated with more money that a player has won. This is really a positive relationship, but it looks negative because the more money, the better, while the lower the scoring average, the better..594 between driving distance and drive accuracy. This is a true negative relationship. Longer drives are associated with not hitting as accurately..52 between average score and world rank is another highly positive relationship. There are several moderate relationships:.439 between putts per round and sand saves percentage. That is, fewer putts per round are associated with a higher percentage of sand saves..373 between driving distance and money earned, reflecting that generally hitting longer drives is associated with earning more money..367 between drive accuracy and earning more money. This reflects a positive association between these two variables. Finally, there are some relationships that are low and unimportant:.3 between drive accuracy and scrambling.29 between driving distance and putts per round.33 between money won and % sand saves Table. Correlation Matrix Among all Variables (N = 3) Variable s Mon ey won World rank Avera ge score Drive distan ce Drive accura cy Greens in regulati Putts per round Scrambli ng Sand saves From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

13 on Money won..77* ** -.7** *.373*.367* World rank..52* **.3.36* * Average score Drive distance ** * ** -.2 Drive accuracy (%) **.3.77 Greens in regulatio n (%)..549* * Putts per round..449*.439 * Scrambli ng..569* ** Sand saves (%). ***p <. **p <. *p <.5. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

14 Using Regression in Prediction In chapter we discussed regression, which is the correlation between two variables and the fact that a straight line may be used to fit the data set as in figure.. The data (DV = drive distance, IV = drive accuracy) for this example are shown below in figure.3. You can observe that the relationship is negative. Longer drives are associated with lower accuracy. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

15 Figure.3 Negative relationship between drive distance and drive accuracy. In SPSS we do the following: Click on the Analyze pull-down bar. Click on Regression. Click on Linear. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

16 Enter driving distance as the dependent variable and driving accuracy as the independent variable. That is, we want to develop a regression (with a prediction equation) for estimating driving distance from driving accuracy. Click OK. You will first see a table similar to table.2 that shows the relationship (prediction) between the two variables. Table.2 Model Summary Model r r 2 Adjusted r 2 Standard error of the estimate.594 (a) a Predictors: (Constant), drive accuracy. Table.2 shows the calculated r =.594 and r 2 =.353; 35% of the variance in drive distance is associated with drive accuracy. Note the standard error of the estimate is Table.3 shows the test of that correlation (i.e., is it significant?). You can see that the correlation is significant as the F (,2) = 5.29, p <.. Table.3 ANOVA(b) Model Sum of squares df Mean square R Significance Regression (a) Residual Total From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

17 a Predictors: (Constant), drive accuracy. b Dependent variable: drive distance. Table.4 is the prediction equation: Y = X Table.4 Coefficients(a) Unstandardized coefficients Standardized coefficients Model B Standard error Beta t Significance (Constant) Drive accuracy a Dependent variable: drive distance. Or you can calculate a predicted score by taking 34. and subtracting the drive accuracy times.94. For example, Rod Pampling s drive accuracy percentage is If we multiply , we get 6.7. Subtract 6.7 from 34. and the estimated distance for Rob Pampling is 27.. His real average distance is 2, so you can see our estimated score is very close to his real score. Remember, all we are doing here is estimating the straight line based on the average data for each variable for all the golfers. However, this estimate has to be considered as plus or minus the standard error of the estimate (given previously as 6.37) that we showed you how to calculate in chapter. Thus, we would expect his actual average score to fall between and 2.7 and, in fact, it does. Using Multiple Regression Multiple regression is similar to regression except there is more than one predictor variable in the multiple regression that is calculated. In the previous section where we used regression, the predictor (or X) variable was drive accuracy and the criterion variable was drive distance (or Y). In this part we will use several predictors (X variables) money won, average score, drive distance, drive accuracy, greens hit in regulation, scrambling, and sand saves to putts per round (single criterion, or Y variable). In SPSS, do the following: Click on the Analyze pull-down menu. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

18 Click on the Regression bar. Click on the Linear bar. Enter the dependent variable (putts per round) and the independent variables (money won, average score, drive distance, drive accuracy, greens hit in regulation, scrambling, and sand saves). Change Method (below the Independent(s) box) to Forward. Click OK. The forward method means the program selects the best single predictor first, then the second best predictor (after variance accounted for by the first predictor is removed), and so on, until there are no predictors that contribute significantly to explaining variance associated with money earned. If you return to table. and look at the correlation of each variable with putts per round, you can see that greens in regulation is the best single predictor (.549). Thus, that is the variable that will be selected first in multiple regression. The question then is what variable(s) will still significantly predict putts per round when the variance associated with the relationship between greens in regulation and putts per round has been considered? Information summarized from the SPSS output in table.5 shows that, in addition to the contribution made by greens in regulation (3.2% of the variance accounted for in putts per round), average score accounted for an additional 2.4% (which was significant), bringing the total variable accounted for by the two predictors to 5.6%, which was significant, F(2,27) = 3.55, p <.. None of the remaining predictors accounted for any significant portion of the variance after these two (greens in regulation and average score) were used in the equation. Table.5 Contribution to Putts Per Round Model r r 2 r 2 chance Step Greens in regulation Step 2* Average score *F(2,27) = 3.55, p <. (test of the total linear combination). If one wanted to use this weighed combination of greens in regulation plus average score to predict putts per round, the regression equations would be as follows: Y = (greens in regulation) +.43 From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

19 (average score) You can have students run this example (or any other combination of predictors and criterion) by using the steps listed previously. Chapter 9 Differences Among Groups In this section we continue to use the data on professional golfers to provide SPSS examples of calculating differences among groups. Our grouping variable will be the level of performance on the PGA tour: group is top money winners, group 2 is money winners ranked 2 to 3, and group 3 is money winners ranked 4 to 5. The last column in the data set has numbers assigned matching those groupings. Independent t Test This analysis using SPSS compares the means of the top money winners (group ) with the players ranked 2 to 3 (group 2) on average birdies per round. The means and standard deviations for the two groups are as follows: Players ranked to : M = 69.53, SD =.3 Players ranked 2 to 3: M = 7.56, SD =.4 t() = 6.46, p =. To run these same data on SPSS, do the following: Click on the Analyze drop-down menu. Click on the Compare Means bar. Select Independent t test. Enter the Test Variable of average score and the Grouping Variable of grouping by money. Click on Define Groups and enter and 3 to indicate the two groups. Click OK to run the analysis. One-Way (Simple) Analysis of Variance (ANOVA) In this analysis we will compare all three groups: top players (), players ranked 2 to 3 (2), and players ranked 4 to 5 (3) on driving distance. As you can see from the following results, the outcome is quite interesting: From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

20 Players ranked to : M = 294.5, SD = 5.2, confidence intervals = 2.4 to 3.9 Players ranked 2 to 3: M = 27.4, SD = 5., confidence intervals = to 296. Players ranked 4 to 5: M = 29., SD =.3, confidence intervals = 277. to 39.7 Despite our intuition, the three groups are not different with an F(2, 27) = 2.3, p =.. This is confirmed by the Bonferroni tests. Interestingly, the second group has the lowest mean, but because of the relatively large standard deviations there are no differences. To run these same data on SPSS, do the following: Click on the Analyze drop-down menu. Click on the Compare Means bar. Select One-Way ANOVA. Enter the Dependent List of driving distance and the Grouping Variable of grouping by money. Click on Posthoc and check Bonferroni and then click Continue. Click OK to run the analysis. We should note that we got the descriptive statistics by using Analyze, Descriptive Statistics, and Explore combination that we reviewed in chapter 6. Chapter Nonparametric Techniques In using nonparametric procedures, SPSS easily permits data transformation to ranks and has a variety of procedures for completing nonparametric statistics. When data are not normal, these statistics would be used. For example, money won has a rather unusual distribution (see figure.). From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

21 Figure. Histogram for money earned per golfer. For money won, skewness (.7) is above expectations for normal data (the kurtosis =.252). Based on this information, and to make the assignment more interesting, we can change the variables, money won and drive accuracy, to ranks using the SPSS by doing the following: Use the Transform pull down menu. Click the Rank Cases bar. Enter the two variables (money won and drive accuracy). From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.

22 Click OK to transfer the data to ranks. This procedure results in two new columns of data on the SPSS data sheet that are the two variables with data ranked. To do a nonparametric correlation in SPSS, do the following: In the Analyze pull-down menu, click on Correlate. Click on Bivariate. Enter the ranked variables: rank of money won, and rank of drive accuracy. Check the box for Spearman to do a Spearman s rank-order correlation. Click OK to run the analysis. If we return to the correlation matrix presented as table., we can see that the correlation between these two variables using the original data is.367, while the correlation using ranked data is.3. If we square each of those (.367 squared = 3.5% of variance;.3 squared = 66.% of variance), the gain in variance accounted for by changing the non-normal data to ranks was 52.6%, or nearly four times as large. The nonparametric statistic is large and the significant value is much larger, demonstrating the reasons nonparametric statistics are valuable. From J.R. Thomas, J.K. Nelson, and S.J. Silverman. 25, Research methods in physical activity instructor guide, 7th ed.