PSYC354 Homework 3 complete solutions correct answers key

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_______.

2)

What is an outlier?

__An observation that lies an abnormal distance from other values in a random sample from a population.______

3)

Which measure of central tendency is most likely to be adversely affected by outliers?

__variance______

4)

We compute standard deviation by taking the __square root______ of the variance.

 

Question 5a-5d

For the following terms, write the equivalent mathematical symbol (letter or letters) for the sample statistic.

5-a)  Score:

                           RX

5-b)  Mean:

                           M

5-c)  Standard deviation:

                             SD2 & s2

5-d)  Number of participants in sample:

1

 

 

Question 6a-6c

These are the scores of eleven patients on the Beck Depression Inventory (BDI ® ). Scores can range from 0 to 63.

12

19

11

23

16

15

27

25

52

13

14

 

6-a)  What is the mean of the scores? (Compute this using a calculator):  

Answer 20.636363636364

6-b)  What is the median of these scores?

Answer 16

6-c )  Compare the mean and median. Does the difference between them suggest that the data are skewed very much?
Explain.

Answer The data is skewed, I would say by a considerable amount.

Explanation/ Justification The mean is the average so it may be more accurate, data wise, to take the mean over the median since it is not very lose to the mean in this case.

 

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)     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
 

7-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?

 

Answer The line graph for Manhattan shows high variability.

 

Answer The level of variability tells us that the household income of this area of Manhattan varies drastically. It shows that some households may be living at poverty level for the cost of living in this area. It also could mean that the career paths chosen by heads of households are also extremely variable.

 

7-c)     Click on Line 6. Though both boroughs depicted show some variability, which borough (not a street) shows the most variability in median household income?

 

Answer
Manhattan

 

7-d)     On Line 3, find the following two subway stops: New Lots Ave. (the first of the Brooklyn stops) and Park Place (the first of the highest stops in Manhattan). What is the difference (calculate) between the median household incomes of the two areas?

 

Answer
159,423

 

7-e)      Click on the “F” line. Which subway stop in Brooklyn seems to be an outlier?

 

Answer
York St.

 

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 central tendency?

 

Answer

I think the author chose the median because it’s more consistent and represents the average of all house holds and resembles less of a variance per stop.

 

 

 

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 ( 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
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
4)

Create a histogram to show the distribution of the anxiety scores.
Edit the graph so that most of the normal curve is visible.

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 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

649    654    652    675    660    667    675    668    681    671

685    692    676    689    683    700    692    688    688    694

Men

825   818    813    831    822    851    815    816    833    827

830    828    833    846    837    851    868    831    881    854

 

 

1)

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)

 

 

2)

Create a boxplot describing the average overall weekly salary for each gender.

Answer- SPSS boxplot:

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?

Answer

 

 

 

Part IV: Cumulative

Questions 1-4

BDI Scores

9

10

9

5

17

3

15

20

17

62

15

12

10

4

61

61

22

15

10

11

·         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).

 

 

 

1)

Using SPSS, run a frequencies analysis on these scores that includes:

·         A Frequency Table

·         Table of Descriptive Statistics

o   Include measures of central tendency, dispersion/spread, 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:

 

 

2)

Create a graph to describe the data set.

Justify why this graph is the best choice for these data.

Answer- SPSS graph

 

Explanation/ Justification

3)

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

 

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!