PSYC 354 HOMEWORK 3 Central Tendency and Variability When submitting this file, be sure the filename includes your full name, course and section. Example: HW3_JohnDoe_354B01 Be sure you have reviewed this module/week's lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Part I: Concepts Questions 1-7 These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. Questions 1-4 Fill in the highlighted blanks to answer/complete the statements. 1 ) The arithmetic average of a set of numbers is the ________. What is an outlier? 2) ________ 3 ) 4 ) Which measure describes the typical amount or distance a score deviates from the mean in any given distribution? ________ What is the mathematical relationship between variance and standard deviation? ________ Question 5 For the following terms, write the equivalent mathematical symbol (letter or letters) for the sample statistic. 5-a) Standard deviation: Answer 5-b) Mean: Answer Page 1 of 6 PSYC 354 5-c) Score: Answer 5-d) Number of participants in sample: Answer Question 6a-6c These are the winning percentages for 11 baseball players for each one's best 4-year pitching performance: 0 . 0.72 0.70 0.77 0.78 0.74 0.31 0.81 0.61 0.65 6-a) 7 1 8 3 2 7 2 7 7 5 5 What is the mean of the scores? (Compute this using a calculator): 0.651 Answer 6-b) What is the median of these scores? Answer 6-c ) Compare the mean and median. Does the difference between them suggest that the data are skewed very much? Explain. Answer Explanation/ Justification Question 7 Recall the interactive graph from Homework 2 depicting household income and location in New York City. Page 2 of 6 PSYC 354 Based on this module/week's reading, why do you think the author of this graph chose the median household income instead of the mean household income to describe central tendency? Explanation/ Justification Part II: SPSS Analysis Green and Salkind Course Text, Lesson 21: Exercises 1, 4, 7, and 8 Questions 1 and 4 o Green and Salkind Text, Lesson 21 o Lesson 21 Exercise File 1 (located under course's Assignment Instructions folder) Part II: Exercises 1a-1d and Exercise 4 Green and Salkind, Lesson 21, Exercises 1 and 4 Open \"Lesson 21 Exercise File 1\" in order to complete these exercises. David collects anxiety scores from 15 college students who visit the university health center during finals week: 1) Compute descriptive statistics on the anxiety scores. From the output, identify the following: a. Skewness b. Mean c. Standard deviation d. Kurtosis Answer: SPSS Table- Descriptive Statistics for Anxiety Scores (paste Table in this cell) 1-a) Skewness: Answer 1-b) Mean: Answer 1-c) Standard deviation: Answer 1-d) Kurtosis: Answer Create a histogram to show the distribution of the anxiety scores. 4) Edit the graph so that most of the normal curve is visible. Page 3 of 6 PSYC 354 Answer: SPSS Figure- Histogram for Anxiety Scores with Normal Curve (paste Figure in this cell) Part III: SPSS Data Entry and Analysis Data provided below. The steps will be the same as the ones you have been practicing in Part I of the assignment; the only difference is that you are now responsible for creating the data file, as well. Remember to do the following: a) Name and define your variables under the Variable View, then return to the Data View to enter the data; and b) Paste all SPSS output and graphs into your homework file at the appropriate place. Part III: Questions 1-4 The following data are taken from the Bureau of Labor Statistics surveys from the years 2009-2013. They represent the average weekly pay for wage and salary earners measured at 4 different quarters each year and broken down by gender. Enter these data into a new file containing one variable for gender and one variable for salary. For the gender variable, code women as 1 and men as 2 o Remember to define these in Value Labels. o There will be twenty \"1\"s and twenty \"2\"s (as many participants as in each group). The corresponding scores will be entered in the salary column (second column). If you need an example, look at the set-up of gender in the \"Lesson 21 Practice Data File 1\" document. Women 649 652 657 670 683 689 673 688 657 665 672 662 679 669 684 697 689 685 692 691 Page 4 of 6 PSYC 354 Men 823 829 815 812 825 819 844 810 813 830 824 825 827 843 832 848 865 828 875 854 In SPSS, compute descriptive statistics for each gender for these data. These steps, among others, are covered in this module/week's SPSS tutorial. 1) Answer- SPSS Table- Descriptive Statistics for Weekly Pay by Gender: (Paste one table; should include weekly pay grouped by men and women) Create a boxplot describing the average overall weekly salary for each gender. Answer- SPSS boxplot: 2) Based on these data, what is the mean weekly income for women? 3) Answer 4) What is the standard deviation of the weekly income for men? Answer Part IV: Cumulative Questions 1-4 The BDI (Beck et al., 1961) is an instrument widely used to assess levels of depression in individuals in a variety of settings. The scores range from 0-63 (whole numbers only). A researcher administers the BDI to a sample of college students. The results appear in the table below. They are entered as 2 columns to save space (i.e., you will not need 2 columns in the SPSS file). BDI Scores 9 10 9 8 19 3 14 21 17 62 15 12 10 4 10 21 23 18 17 61 Page 5 of 6 PSYC 354 1) Using SPSS, run a frequencies analysis on these scores that includes: A Frequency Table Table of Descriptive Statistics o Include central tendency, dispersion, and distribution. Paste the output into your homework file. Answer- SPSS Table- Frequency Table for BDI Scores: Answer- SPSS Table- Descriptive Statistics for BDI Scores: Create a graph to describe the data set. Justify why this graph is the best choice for these data. Answer- SPSS graph 2) Explanation/ Justification What is the skewness of this data set? What does this mean? Answer 3) Explanation 4) Based on your graph and your answers above, which measure of central tendency is most appropriate for describing this group of scores? Why? Answer Explanation/Rationale Submit Homework 3 by 11:59 p.m. (ET) on Monday of Module/Week 3. Remember to name file appropriately. Done! Page 6 of 6 $FL2@(#) IBM SPSS STATISTICS 64-bit MS Windows 22.0.0.0 #########################Y@13 Jul 1519:57:32 ###########################HEIGHT ####Height in inches########################WEIGHT ####Weight in pounds############################################################# ############################################ p= P@q= @`Hz#wP@#Q#]@R#P@{#GJ[@(\\/Q@Gz##_@#QP@Q#a@= p}P@$`@Q# %Q@Hz#_@(\\P@{#G:^@Gz#P@_@Q##Q@Gz#^Y@\\(Q@Hz##b @z#GaP@ = [@ pP@Q#`@ p=P@{#GJb@ p=jQ@{#G2b@33333sP@(\\5^@p= P@R#\\@(\\#Q@ `@z#G#Q@Gz#_@)\\Q@#Q_@ PSYC 354 HOMEWORK 2 Frequency Tables and Graphs When submitting this file, be sure the filename includes your full name, course and section. Example: HW2_JohnDoe_354B01 Be sure you have reviewed this module/week's lessons and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Part I: Concepts All Questions These questions are based on the Nolan and Heinzen reading and endofchapter questions. Use the following table to answer Question 1. This table depicts the scores of 83 students on an exam worth 65 points. 1) Use the information in the table to determine the percentages for each interval. Depending on your rounding decisions, these may or may not add up to exactly 100% but should be very close. Table: Grouped Frequency Table Exam score Frequency 60-62 57-59 54-56 51-53 48-50 45-47 42-44 TOTAL 3 9 21 18 14 10 8 83? Percentages for each Interval 3.6%? 10.8%? 25.3%? 21.7%? 16.9%? 12.0%? 9.6%? 99.9%? 2) When constructing a histogram and labeling the x- and y-axes, the lowest number on each axis should ideally be ___zero_____. 3) A frequency distribution that is bell-shaped, symmetrical, and unimodal is ____ normal distribution___________. ________. 4) A frequency distribution that has a tail trailing off to the right of the distribution is _____positively skewed__________. _________. Page 1 of 10 PSYC 354 5) A frequency distribution of ages of residents at a senior citizen home is clustered around 83 with a long tail to the left. This distribution is _____ negatively skewed________. 6) When a variable cannot take on values above a certain level, this is known as a(n) ___ ceiling______ effect. 7) A grouped frequency table has the following intervals: 30-44, 45-59, and 60-74. If converted into a histogram, what would the midpoints be? 30-44: Midpoint Value 37.5 45-59: Midpoint Value 52.5 60-74: Midpoint Value 67.5 8) Do the data below show a linear relation, non-linear relation, or no relation at all? Answer Linear Relation 9) Do the data below show a linear relation, non-linear relation, or no relation at all? Answer No relation at all Page 2 of 10 PSYC 354 Part I: Question 10a- 10e At this website, (http://projects.newyorker.com/story/subway/) you will find an interactive graph concerning New York City's geography and income. Read the introduction and click on different \"subway lines\" to see how the interactive graph works. Note that the abbreviations stand for the four different boroughs: MAN = Manhattan BRX = Bronx BRK = Brooklyn QNS = Queens Also note that hovering your mouse over the dots on the graph displays the subway stop and the median income of households in that area. 10-a) In which of the four boroughs is the median household income highest? (This is made evident as you click on the different lines.) Answer Manhattan 10-b) Click on the \"A\" line. Does the line graph for Manhattan show high or low variability? What does this level of variability tell us about the household income in this area of Manhattan? AnswerHigh Variability Answer People make different salaries, from $31,875 to $205,192 10-c) Click on line 2. Which borough (not a street) shows the least variability in median household income? Answer Bronx 10-d) On line 2, find the following two subway stops: Park Place (the first of the highest Manhattan stops) and E 180 St. (one of the lowest Bronx stops, located about halfway across the BRX section). What is the difference (calculate) between the median household incomes of the two areas? Answer Park Place = $205,192 E 180 St. = $13,750 Difference = $191,442 10-e) Click on the \"D\" line. Which subway stop in Brooklyn seems to be an outlier? Answer Atlantic Ave./Barclays Center (much higher than the other Brooklyn stops Page 3 of 10 PSYC 354 Part II: SPSS Analysis Green and Salkind, Lesson 20 Open the \"Lesson 20 Exercise File 1\" document (found in the course's Assignment Instructions folder) in order to complete these exercises. Always use the Blackboard files instead of the files on the Green and Salkind website as some files have been modified for the purposes of this course. Reminder: For Exercise 1, be sure to paste in the SPSS output and write out the answers for A, B, and C beneath it. Part II: Questions 1-4 Ann wants to describe the demographic characteristics of a sample of 25 individuals who completed a large-scale survey. She has demographic data on the participants': Gender (two categories) Educational level (four categories) Marital status (three categories) Community population size (eight categories). Questions 1a -1c 1) Conduct a frequency analysis on the gender and marital status variables. From the output, identify the following: a. Percentage of men b. Mode for marital status c. Frequency of divorced people in the sample Answer- Table- Gender: (paste Table in this cell) Gender Frequency Valid Percent Valid Percent Men 13 52.0 52.0 Women 12 48.0 48.0 Total 25 100.0 100.0 Page 4 of 10 PSYC 354 Answer- Table- Marital Status: (paste Table in this cell) Marital Status Frequency Valid Percent Valid Percent Married 9 36.0 Divorced 11 44.0 5 20.0 25 100.0 Never Married Total 1-a) Percentage of men: Answer52% 1-b) Mode for marital status: Answer Divorced Mode of marital status is \" Divorced\" since this has highest frequency (11) 1-c) Frequency of divorced people in the sample: Answer11 Questions 2-4 2) Create a frequency table to summarize the data on the educational level variable. Page 5 of 10 PSYC 354 Answer- Table- Education Level: (paste Table in this cell) Education Level Frequency Valid Did not graduate from high Percent 6 24.0 High School Graduate 4 16.0 Bachelor's Degree 8 32.0 Post Graduate Degree 7 28.0 25 100.0 school Total 3) Create a bar chart to summarize the data from the community population variable. Page 6 of 10 PSYC 354 Answer- Bar chart - Community population: (paste Bar chart in this cell) 4) Write a Participants section describing the participants in Ann's s ample. Answer- Participants Section: Ann's sample has randomly selected 25 participants. The participants are categorized demographically in four ways. According to Gender, 52% are males and rest females. According to the marital status, 44% of are divorced and next married (36%) and the remaining are unmarried ones. Education wise, most of the participants completed high school or above (76%) and only 24% are not even completed high school. According to the community population, highest percentage of people are from the size 1,001 to 5,000. Page 7 of 10 PSYC 354 Part III: SPSS Data Entry and Analysis The steps will be the same in Part III as the ones you have been practicing in Part I of the assignment; the only difference is that you are now responsible for creating the data file as well. Remember to do the following: Name and define your variables under the \"Variable View,\" then return to the \"Data View\" to enter the data; and Paste all SPSS output and graphs into your homework file at the appropriate place. Part III: Questions 1a-1c This question is based on the data in the end-of-chapter Question 2.30 of the Nolan and Heinzen textbook. Create a variable called \"num_years\" in a new SPSS file. Enter the data given in #2.30. o Remember to enter the data into 1 column (variable). 1-a) Run a frequencies analysis that includes descriptive statistics for these scores (central tendency, dispersion, and distribution) and create a frequency table in SPSS for these data. Answer- Descriptive Statistics Table- Number of Years: (paste Table in this cell) Descriptive Statistics Std. N Minimum Maximum Mean Deviation Statisti c Statistic num_years 42 Valid N (listwise) Statistic Statistic 6.00 15.00 8.2143 Statistic 2.44486 42 Page 8 of 10 PSYC 354 Answer- Frequency Table- Number of Years: (paste Table in this cell) num_years Frequency Valid Percent Valid Percent 6.00 10 23.8 23.8 7.00 11 26.2 26.2 8.00 9 21.4 21.4 9.00 4 9.5 9.5 10.00 2 4.8 4.8 11.00 1 2.4 2.4 12.00 1 2.4 2.4 13.00 1 2.4 2.4 14.00 1 2.4 2.4 15.00 2 4.8 4.8 Total 42 100.0 100.0 1-b) Create a histogram for these data. Page 9 of 10 PSYC 354 Answer- Histogram - Number of Years: (paste Figure in this cell) 1-c) How many schools have an average completion time of 8 years or less? An average completion time of 10 years or more? Answer for 8 years or less = 30 Answer for 10 years or more =8 Submit Homework 2 by 11:59 p.m. (ET) on Monday of Module/Week 2. Remember to name file appropriately. Done! Page 10 of 10 PSYC 354 HOMEWORK 3 Central Tendency and Variability Be sure you have reviewed this module/week's lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Number all responses. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Review the \"Homework Instructions: General\" document for an example of how homework assignments must look. Part I: Concepts These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. 1. The arithmetic average of a set of numbers is the prefreerd measure of central tendency. 2. What is an outlier? An outlier is an extreme score that is either very high or very low in comparison with the rest of the scores. 3. Which measure describes the typical amount or distance a score deviates from the mean in any given distribution? The standard deviation describes the typical amount or distance a score deviates from the mean in any given distribution. 4. What is the mathematical relationship between variance and standard deviation? 5. For the following terms, write the equivalent mathematical symbol (letter or letters) for the sample statistic. a. Standard deviation is represented symbolically by . b. Mean is represented symbolically by . c. Score is represented symbolically by . d. Number of participants in sample represented symbolically by . 6. These are the winning percentages for 11 baseball players for each one's best 4-year pitching performance: 0.755 0.721 0.708 0.773 0.782 0.747 0.477 0.817 0.617 0.650 0.651 a. What is the mean of the scores? (Compute this using a calculator.) Page 1 of 11 PSYC 354 The mean of the scores is 0.6998. b. What is the median of these scores? The median of the scores is 0.721. c. Compare the mean and median. Does the difference between them suggest that the data are skewed very much? The difference between mean and median is -0.0212. The difference between them is significantly very low, it suggest that the data are not skewed very much. Score 0.755 0.721 0.708 0.773 0.782 0.747 0.477 0.817 0.617 0.650 0.651 Mean 0.6998 Median 0.721 7. Recall the interactive graph from Homework 2 depicting household income and location in New York City. Based on this module/week's reading, why do you think the author of this graph chose the median household income instead of the mean household income to describe central tendency? Page 2 of 11 PSYC 354 Generally the data on household income in a locality has extreme values, which can vary considerably large among themselves. In such situations using the mean household income to describe central tendency is not appropriate as mean has influenced by extreme values more. In such situations we need to use a measure of central tendency that can less influenced by extreme observations. Median is one such measure of central tendency as it is a measure of location. So in this context the author of this graph chose the median household income instead of the mean household income to describe central tendency. Part II: SPSS Analysis 1. Green and Salkind, Lesson 21, Exercises 1, 4 Open the \"Lesson 21 Exercise File 1\" document (found in the course's Assignment Instructions folder) in order to complete these exercises. Ex 1. Compute descriptive statistics on the anxiety scores. From the output, identify the following: (a) Skewness, (b) Mean, (c) Standard deviation, and (d) Kurtosis. (a) Skewness = .416 (b) Mean = 32.27 (c) Standard deviation = 23.478 Page 3 of 11 PSYC 354 (d) Kurtosis = -1.124 Ex 2. Compute percentile ranks on the anxiety scores assuming that the distribution is normal. What are the scores associated with the percentile ranks of 12, 27, 38, 73, and 88? The scores associated with the percentile ranks of 12, 27, 38, 73, and 88 are respectively 5, 18, 25, 47 and 60. The percentile ranks on the anxiety scores assuming that the distribution is normal are shown in the table below: Ex 3. Compute percentile ranks on the anxiety scores not assuming that the distribution of scores is normal. The percentile ranks on the anxiety scores not assuming that the distribution of scores is normal are shown in the table below: Page 4 of 11 PSYC 354 Ex 4. Create a histogram to show the distribution of the anxiety scores. Edit the graph so that most of the normal curve is visible. The histogram to show the distribution of the anxiety scores is given below: Page 5 of 11 PSYC 354 2. Green and Salkind, Lesson 21, Exercises 7-8 Open the \"Lesson 21 Exercise File 2\" document (found in the course's Assignment Instructions folder) in order to complete these exercises. Note: The total attitude scores mentioned in #6 are already computed and included in the exercise file. Part III: SPSS Data Entry and Analysis 1. The following data are taken from the Bureau of Labor Statistics surveys from the years 2009-2013. They represent the average weekly pay for wage and salary earners measured at 4 different quarters each year and broken down by gender. Enter these data into a new file containing one variable for gender and one variable for salary. For the gender variable, code women as 1 and men as 2; remember to define these in Value Labels. There will be twenty \"1\"s and twenty \"2\"s (as many participants as in each group). The corresponding scores will be entered in the salary column. If you need an example, look at the set-up of gender in the \"Lesson 21 Practice Data File 1\" document. Women Men 649 683 823 829 652 657 670 657 665 672 662 679 689 673 688 684 697 689 685 692 815 812 825 819 844 810 813 825 827 843 832 848 865 828 669 691 830 824 875 854 In SPSS, compute descriptive statistics for each gender for these data. These steps, among others, are covered in this module/week's SPSS tutorial. Remember to copy and paste output. a. Table 1 contains the descriptive statistics for each gender for these data. Table 1 Page 6 of 11 PSYC 354 b. Create a boxplot describing the average overall weekly salary for each gender. The following is the comparative box-plots describing the average overall weekly salary for each gender. Page 7 of 11 PSYC 354 c. Based on these data, what is the mean weekly income for women? The mean weekly income for women is $675.15. d. What is the standard deviation of the weekly income for men? The standard deviation of the weekly income for men is $17.686. If you were to conduct a statistical test to compare these two data sets (men and women), would it be more informative to compare the means of the groups or the ranges of the groups? Why? e. Since the data measured on interval level, the statistical test to compare the means of the groups would be more informative. The steps will be the same as the ones you have been practicing in Part I of the assignment; the only difference is that you are now responsible for creating the data file, as well. Remember to do the following: a) Name and define your variables under the Variable View, then return to the Data View to enter the data; and b) Paste all SPSS output and graphs into your homework file at the appropriate place. Page 8 of 11 PSYC 354 Part IV: Cumulative The BDI (Beck et al., 1961) is an instrument widely used to assess levels of depression in individuals in a variety of settings. The scores range from 0-63 (whole numbers only). A researcher administers the BDI to a sample of college students. The results appear in the table below. They are entered as 2 columns to save space (i.e., you will not need 2 columns in the SPSS file). BDI Scores 9 10 9 8 19 3 14 21 17 62 15 12 10 4 10 21 23 18 17 61 1. Using SPSS, run a frequencies analysis that includes a frequency table and descriptive statistics for these scores. Include central tendency, dispersion, and distribution. Paste the output into your homework file. Table 2 contains the frequency distribution of the given BDI scores. Table 2 BDI Scores (Binned) Valid 1 (0-5) 2 (6 -10) 3 (11 - 15) 4 (16 - 20) 5 (21 - 25) 6 (26 +) Total Frequency Percent 2 10.0 6 30.0 3 15.0 4 20.0 3 15.0 2 10.0 20 100.0 Valid Percent 10.0 30.0 15.0 20.0 15.0 10.0 100.0 Cumulative Percent 10.0 40.0 55.0 75.0 90.0 100.0 Table 3 contains the descriptive statistics for the given BDI scores. Table 3 Page 9 of 11 PSYC 354 Descriptive Statistics BDI Scores (Binned) N Valid Missing Mean Median Std. Deviation Variance Skewness Std. Error of Skewness Kurtosis Std. Error of Kurtosis Range 20 0 3.30 3.00 1.559 2.432 .276 .512 -1.029 .992 5 2. Create a graph to describe the data set. Justify why this graph is the best choice for these data. The following is the histogram that describes the frequency distribution constructed to the given BDI Scores. Page 10 of 11 PSYC 354 3. What is the skewness of this data set? What does this mean? The skewness of this data set is 0.276. It indicates that graph of the constructed frequency distribution is positively skewed. 4. What is the kurtosis of this data set? What does this mean? The kurtosis of this data set is -1.029. It indicates that graph of the constructed frequency distribution is flatter than the normal curve. 5. Based on your graph and your answers above, which measure of central tendency is most appropriate for describing this group of scores? Why? Based on the histogram and the answers above, the mean BDI scores is the most appropriate measure of central tendency for describing this group of scores, since the data doesn't contain any outliers. Submit Homework 3 by 11:59 p.m. (ET) on Monday of Module/Week 3. Page 11 of 11