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 ) Another name for the arithmetic average of a set of numbers is the ____mean____. Name the three measures of central tendency covered in Chapter 4 of Nolan and Heinzen (2016). 2) 1.__mean__ 3 ) 4 ) 2. median and 3. mode ____ According to the text and presentation, which measure of central tendency is most likely to be negatively affected by outliers? ____mean____ Which measure of variability is defined as the typical amount that each score varies from the mean? ___standard deviation_____ Question 5a-5d For the following terms, write the equivalent mathematical symbol (letter or letters) for the sample statistic. 5-a) Score: X 5-b) Mean: M Page 1 of 9 PSYC 354 5-c) Standard deviation: SD 5-d) Number of participants in sample: N Question 6a-6c These are the scores of eleven patients on the Beck Depression Inventory (BDI ). Scores can range from 0 to 63. 1 0 19 6 8 14 16 26 25 54 12 20 6-a) What is the mean of the scores? (Compute this using a calculator): 19.1 6-b) What is the median of these scores? 16 6-c ) Compare the mean and median. Does the difference between them suggest that the data are skewed positively, skewed negatively, or symmetrical? Explain. POSITIVE SKEW If the mean is pulled up then the median is pulled by a posiyve score ending in a positive skew. Page 2 of 9 PSYC 354 Question 7a- 7f 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. 7-a) Click on Line 5. In which of the boroughs shown is the median household income highest? Manhattan 7-b) Click on the \"C\" 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? High variability There is a drastic level of income inequality from over 200k to under 50k 7-c) Click on Line 6. Though both boroughs depicted show some variability, which borough (not a street) shows the least variability in median household income? Manhattan shows the most variability 7-d) On Line 2, find the following two subway stops: Park Place (the first of the two highest Manhattan stops) and 149 St.-Grand Concourse (the first of the Bronx stops). What is the difference (calculate) between the median household incomes of the two areas? 188,612 7-e) Click on Line 5. Which subway stop in Manhattan seems to be an outlier? Broklyn Bridge City Hall 7-f) 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 the central tendency of this data? Answer The variability is easier to see when using the median because the the median is the middle of the data. Page 3 of 9 PSYC 354 Part II: SPSS Analysis Green and Salkind Course Text, Lesson 21: Exercises 1 and 4 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 ( do not complete numbers 2 or 3) 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 Page 4 of 9 PSYC 354 Answer: SPSS Table- Descriptive Statistics for Anxiety Scores (paste Table in this cell) Statistic Anxiety Scores Mean 32.27 95% Confidence Interval for Lower Bound 19.27 Mean Upper Bound 45.27 5% Trimmed Mean 31.24 Median 25.00 Variance 6.062 551.210 Std. Deviation 23.478 Minimum 5 Maximum 78 Range 73 Interquartile Range 40 Skewness Kurtosis 1-a) Skewness: 1-b) Mean: Std. Error .416 .580 -1.124 1.121 .416 statistic .580 std error 32.37 1-c) Standard deviation: 23.478 1-d) Kurtosis: -1.124 statistic 1.121 std error 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 5 of 9 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. Page 6 of 9 PSYC 354 Part III: Questions 1-4 The following data are based on numbers taken from the Bureau of Labor Statistics surveys from the years 2009-2013, with some modifications. 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 in column 1, code women as 1 and men as 2 o Remember to define these in Value Labels as covered in presentations since Module 1. o There will be twenty \"1\"s and twenty \"2\"s (as many participants as in each group). The corresponding earnings 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 Men 1) 749 785 925 930 754 752 775 760 767 775 768 781 771 792 776 789 783 700 792 788 788 694 918 913 931 922 951 915 916 933 927 928 933 946 937 951 968 931 981 954 In SPSS, compute descriptive statistics for each gender for these data. The necessary steps are covered in the last 3 slides of this module's SPSS tutorial. 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) 3) Based on these data, what is the mean weekly income for men? Answer 4) What is the standard deviation of the weekly income for women? Page 7 of 9 PSYC 354 Answer Part IV: Cumulative Questions 1-4 1) 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 two columns to save space (i.e., you will not need two columns in the SPSS file, only one). BDI Scores 9 10 9 5 8 3 11 20 11 62 15 12 10 4 61 61 20 15 10 11 Using SPSS, run a frequencies analysis on these scores that includes: A Frequency Table Table of Descriptive Statistics o Include measures of central tendency, variability/spread, and distribution shape. Paste the output into your homework file. Answer- SPSS Table- Frequency Table for BDI Scores: Answer- SPSS Table- Descriptive Statistics for BDI Scores (Include measures of central tendency, variability/spread, and distribution shape): 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 Page 8 of 9 PSYC 354 Based on your SPSS output, what is the numerical skewness value of this data set? What does this value say about how the scores are distributed? 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 9 of 9