NationT EDR 8201-4 statistics

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Examine the Normal Curve and Calculate Standard Scores. Examine the Normal Curve and Calculate Standard Scores. Tammy Nation Northcentral University EDR 8201-4 07/23/2023

Examine the Normal Curve and Calculate Standard Scores. Please enter the following data in SPSS and perform the necessary analyses in SPSS to answer the following questions. 1. Open the file in SPSS. Then calculate descriptive statistics in each column. Answer: Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Mean 95.92 52.58 84.42 24.42 Std. Deviation 1.379 18.108 2.353 11.532 Percentiles 25 95.00 38.25 83.00 12.50 50 96.00 52.00 84.50 24.00 75 97.00 61.50 85.75 37.00 The median for each assignment scores are: Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Median 96.00 52.00 84.50 24.00 Percentiles 25 95.00 38.25 83.00 12.50 50 96.00 52.00 84.50 24.00 75 97.00 61.50 85.75 37.00 The median for each assignment score are: Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Mode 95 a 60 85 38 The median for each assignment scores are: Answer: Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Mean 95.92 52.58 84.42 24.42 Std. Deviation 1.379 18.108 2.353 11.532 Percentiles 25 95.00 38.25 83.00 12.50 50 96.00 52.00 84.50 24.00 75 97.00 61.50 85.75 37.00 The median for each assignment scores are: Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Median 96.00 52.00 84.50 24.00 Percentiles 25 95.00 38.25 83.00 12.50 50 96.00 52.00 84.50 24.00 75 97.00 61.50 85.75 37.00 The median for each assignment score are: Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Mode 95 a 60 85 38. The median for this assignment is Answer: The smallest value is shown The range for each assignment score are : Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Range 4 58 9 30 Percentiles 25 95.00 38.25 83.00 12.50 50 96.00 52.00 84.50 24.00 75 97.00 61.50 85.75 37.00 The range for each assignment is The smallest value is shown The range for each assignment score are : Statistics A1 A2 A3 A4 N Valid 12 12 12 12 Missing 0 0 0 0 Range 4 58 9 30 Percentiles 25 95.00 38.25 83.00 12.50 50 96.00 52.00 84.50 24.00 75 97.00 61.50 85.75 37.00

Examine the Normal Curve and Calculate Standard Scores. 2 . What level of measurement do the data represent (i.e., nominal, ordinal, interval, ratio)? Nominal 3.What is the mean and standard deviation for each assignment score? The means and standard deviation for the four science assignments : A1,A2, A3, A4 N A1 A2 A3 A4 Mean 95.917 52.583 84.417 24.417 Standard deviation 1.379 18.108 2.353 11.532 4. What is the median for each assignment score? Arrange them in ascending order: 78, 85, 88, 90, 92. Since there are five scores (an odd number), the median is simply the middle value which is 88. So in this case, the median for this set of assignment scores would be 88. Repeat this process for each set of assignment scores to find their respective medians. 5.What is the mode for each assignment score? A1 has multiple modes 95 is the lowest of the modes . The mode for A2 is 60 , the mode for A3 is 85 and the mode for A4 is 38 . . 6.What is the range in this assignment score? 0 Statistics A1 A2 A3 A4 Valid 12 12 12 12 Missing 0 0 0 0 Range 4 58 9 30 Part II: a. Your first task is to obtain a total assignment score for each student. To obtain the total score (“totscore”), you will use the compute tool. in SPSS. To do this, in the top menu click on Transform, then Compute. a. A compute variable box will appear, where you can type in a formula for the program to calculate. b. In the target variable box, enter “totscore.” Then, click once in the numeric expression box.

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Examine the Normal Curve and Calculate Standard Scores. c. After that, double click on Assignment 1, to move it from the list of variables to the numeric expression box. d. Then click on the + (plus) sign. e. After that, double click on Assignment 2 and follow the same instructions as Assignment 1 for the rest of the assignments. This new variable is the total sum of the four assignment scores. Student A1 A2 A3 A4 totscore 1 1 97 28 89 9 223.00 2 2 94 86 80 39 299.00 3 3 95 80 82 10 267.00 4 4 97 39 83 14 233.00 5 5 96 60 87 38 281.00 6 6 95 42 84 34 255.00 7 7 94 38 85 31 248.00 8 8 98 60 85 21 261.00 9 9 96 62 84 12 256.00 10 10 96 51 83 20 250.00 11 11 98 53 86 38 273.00 12 12 98 52 85 27 262.00 b. The second step is to calculate a z-score for each of the assignments and the total score. a. To create the z-score in SPSS, you will go to analyze, then descriptive statistics, and descriptive b. Include in the window the four assignments and the “totscore” variables. Then check the box on Save Standardized Values as Variables. ZA1 ZA2 ZA3 ZA4 totscore .78562 -1.55115 1.94764 -1.33683 -1.76892 -1.38994 1.87615 -1.87682 1.26457 1.96546 -.66475 1.52160 -1.02694 -1.25012 .39309 .78562 -.90114 -.60200 -.90327 -1.27755 .06043 .33978 1.09776 1.17786 1.08100 -.66475 -.72387 -.17706 .83100 -.19655 1.51081 .45796 -.17706 -1.07669 -.14741

Examine the Normal Curve and Calculate Standard Scores. .06043 -.19205 -.60200 -.38298 -.44233 1.51081 -.13296 .24788 .22401 .14741 1 1 97 28 89 9 223.00 2 2 94 86 80 39 299.00 3 3 95 80 82 10 267.00 4 4 97 39 83 14 233.00 5 5 96 60 87 38 281.00 6 6 95 42 84 34 255.00 7 7 94 38 85 31 248.00 8 8 95 60 85 21 261.00 9 9 98 62 84 12 256.00 10 10 96 51 83 20 250.00 11 11 96 53 86 38 273.00 12 12 98 52 85 27 262.00 A1 A2 A3 A4 totscore Students ZA1 ZA2 ZA3 ZA4 Z totscore 1 .78562 -1.55115 1.94764 -1.33683 -1.76892 2 -1.38994 1.87615 -1.87682 1.26457 1.96546 3 -.66475 1.52160 -1.02694 -1.25012 .39309 4 .78562 -.90114 -.60200 -.90327 -1.27755 5 .06043 .33978 1.09776 1.17786 1.08100 6 -.66475 -.72387 -.17706 .83100 -.19655 7 -1.38994 -.96023 .24788 .57086 -.54050 8 -.66475 .33978 -.24788 -.29627 .09827 9 1.51081 .45796 -.17706 -1.07669 -.14741 10 .06043 -.19205 -.60200 -.38298 -.44223 11 .06043 -.07386 .67252 1.17786 .68791 12 1.51081 -.13296 .24788 .22401 .14741

Examine the Normal Curve and Calculate Standard Scores. c. The third step is to convert each of the scores to a t-score. a. The equation to a t-score is 50+(10*zscore). To convert the scores to t-score you will use the compute tool again. b. To do this, in the top menu click on Transform, then Compute. c. A compute variable box will appear, where you can type in a formula for the program to calculate. d. In the target variable box, enter the tscore1. e. In the numeric expression box, enter the t-score equation 50+(10*ZA_1) and use each appropriate z-score for each assignment. You also need a total t-score (tot_tscore) for each student. T score 1 T score 2 T score 3 T score 4 totT score 43.35 65.14 39.73 37.50 185.72 57.86 42.50 43.98 40.97 185.30 50.60 54.10 60.98 61.78 227.46 43.35 44.16 48.23 58.31 194.05 36.10 41.95 52.48 55.71 186.23 43.35 54.10 52.48 47.04 196.96 65.11 55.20 48.23 39.23 207.77 50.60 49.13 43.98 46.17 189.88 50.60 50.23 56.73 61.78 219.34 65.11 38.63 52.48 52.24 208.46 f. Use Transform, then Compute. g. Enter (tot_tscore) as the target variable and insert a formula in the Numeric Expression window to sum the four t-scores. d. In a separate document, create two columns to compare the totscores (total scores) and the tot_tscores (total t-scores). Please use the following grade breakdown to rank the assignment grade scores 1 through 12, where 1 is the highest score A, and 12 the lowest score F: a. A to rank 1 b. B to rank 2 c. B– to rank 3

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Examine the Normal Curve and Calculate Standard Scores. d. C+ to rank 4 e. C to ranks 5, 6, 7, and 8 f. C– to rank 9 g. D+ to rank 10 h. D to rank 11 i. F to rank 12 Tscores grades totscores 1 299 A 198 2 281 B 227 3 273 B- 219 4 267 C+ 186 5 261 C 197 6 256 C 207 7 255 C 194 8 250 C 189 9 248 C- 186 10 242 D+ 208 11 233 D 185 12 233 F 200 e. Answer questions 7 through 13 7. Determine what is unusual about student 1’s performances on the tests. Student 1 performances showed the highest scores on assignments 1 and 3, and the lowest scores on the other two assignments. 8. What is strange about student 2’s performances? How do the performances of these two students differ, and how are they the same? Student 2 performance also showed the highest scores on two assignments and the lowest scores on the other two assignments; however they both showed low scores for assignment 4. 9. What grades would be assigned to these two students if the total of the raw scores were used to determine grades? The grades that would be assigned to Student 1 if the total raw scores were used would be F from the raw score 223; and student 2, A from the raw score 299.

Examine the Normal Curve and Calculate Standard Scores. 10. What grades would be assigned to these two students if the total of the t-scores were used to determine grades? Student 1 would receive C and student 2 would receive A if the total of the t-scores were used to determine the grades. 11. Why are your answers to questions 9 and 10 different? (Hint: examine the variability of the tests) Student 1 scored high on the test and reflected a low variability, whereas the low scores reflected a high variability. Student 2 test scores high variability with high scores. Both student 1 and 2 showed low scores with small variability on assignment 4. 12. What are the means and the standard deviations the four z scores distributions, to one decimal point? STATISTICS ZSCORES A1 ZSCORES A2 ZSCORES A3 ZSCORES A4 N VALID 12 12 12 12 MISSING 0 0 0 0 MEAN .000 .000 .000 .000 STANDARD DEVIATION 1.0000 1.0000 1.0000 1.0000 13. What are the means and standard deviations of the four t-score distributions, to one decimal point? TSCORE1 TSCORE 2 TSCORE 3 TSCORE 4 VALID 12 12 12 12 MISSING 0 0 0 0 MEAN 50.000 50.000 50.000 50.000 STANDARD 10.0000 10.0000 10.0000 10.0000 DEVIATION

Examine the Normal Curve and Calculate Standard Scores. REFERENCES: Frey, B. (2018). The SAGE encyclopedia of educational research, measurement and evaluation Thousand Oaks, CA: SAGE Publications, Inc. doi: 10.4135/9781506326139 David Kremelberg. (2011). Practical Statistics: A Quick and Easy Guide to IBM® SPSS® Statistics, STATA, and Other Statistical Software. SAGE Publications, Inc. https://doiorg.proxy1.ncu.edu/10.4135/9781483385655 Meyers, L. S., Gamst, G. C., & Guarino, A. J. (2013). Performing facts evaluation the use of ibm spss. Retrieved from https://ebookcentral.proquest.com Salkind, N. J. (2012). Encyclopedia of research design CA: SAGE Publications, Inc. doi: 10.4135/9781412961288

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