Psychology Statistics

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PSYC 354

Homework 5

Z-Scores

When submitting this file, be sure the filename includes your full name, course and section. Example: HW5_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 1–9

1)

When we standardize scores, we convert individual scores from different normal distributions to a shared normal distribution with a known (a)_____, (b)______, and (c)______.

2)

Define the central limit theorem as described in Nolan and Heinzen (2016).

Answer

3)

A z-score can be thought of as the number of ________ that a score is from the mean.

4)

The formula for the standard error is the ________ divided by the ________ . (Use words, not symbols, to answer this question.)

5) Calculating z scores from raw scores: If a population has a mean of =30 and a standard deviation of  = 3, calculate z scores for each of the following raw scores (X) from this population. Show work on the right hand side, put answers on the left in the space provided.

5a) X = 31; Z = Answer

Work:

5b) X = 27; Z = Answer

Work:

5c) X = 37; Z = Answer

Work:

5d) X = 25.5; Z = Answer

Work:

6) Calculating raw scores from z scores: If a population has a mean of =30 and a standard deviation of  = 3, calculate raw scores (X) for each of the following z scores from this population. Show work on the right hand side, put answers on the left in the space provided.

6a) Z = .57; X = Answer

Work:

6b) Z = -2.03; X = Answer

Work:

6c) Z = -1.0; X = Answer

Work:

6d) Z = 1.68; X = Answer

Work:

7) In a normal curve, what percentage of scores falls:

7a) Above the mean? Answer

Work:

7b) Between the mean and +1 standard deviation (SD) above the mean? Answer

Work:

7c) In the left “tail” of the distribution, more than -2 SD from the mean. Answer

Work:

8) Compute the standard error (m) for each of the following sample sizes, assuming a population mean  50 and a standard deviation of 4.5.

8a) 20 Answer

Work:

8b) 120 Answer

Work:

8c) 1200 Answer

Work:

9) Compute a z-statistic for each of the following sample means, assuming  85 and  9 (Remember to compute M before computing the z statistic!)

9a) A sample of 46 scores has a mean of 89 Answer

Work:

9b) A sample of 82 scores has a mean of 76 Answer

Work:

9c) A sample of 100 scores has a mean of 86. Answer

Work:

Part II: SPSS Analysis

Be sure you have viewed the SPSS tutorial presentation before proceeding.

· Open “Module 5 Exercise File 1” (found in the course’s Assignment Instructions SPSS folder) in order to complete these exercises.

· Reminder: Be sure to paste in the SPSS output and write out the answers in the spaces given.

Part II: Questions 1a-1d

· Open Module 5 Exerise File 1. It contains the IQ scores of 38 participants.

· Compute descriptive statistics of the raw IQ scores

· Create a histogram of the raw IQ scores

· Transform the raw scores to z-scores following the method in the SPSS tutorial and text

· Be sure to save this transformed file, since you will be using it next week as well.

· Identify the z-score that is closest to 0 and farthest from 0.

· Evaluate whether the scores are normally distributed.

· Support your answer.

1a)

Compute Descriptive statistics for the raw IQ scores and paste the table below.

Answer: SPSS: Descriptives table

(paste table in this cell)

1b)

Create a histogram of the raw IQ scores and paste it below.

Answer: SPSS: Histogram

(paste table in this cell)

1c)

Using the descriptives method covered in the presentation and chapter, transform the IQ raw scores to z-scores, creating a new variable.

What is the z-score that is closest to 0 (on either side of the mean) in the data set?

What is the z-score that is the farthest from 0 (on either side of the mean) in the data set?

Answer

Answer

1d)

Based on the histogram from (1b) and your other answers above, would you describe the IQ data as being normally distributed? Why or why not? Support your answer with information from the chapter and presentations regarding normal distributions.

Answer

Justification

Part III: SPSS Data Entry and Analysis

Data provided below.

Stress Index Scores

101

60

10

27

89

60

16

184

34

17

78

141

11

104

76

65

87

19

126

98

Part III: Questions 1a-1d

The data in the column to the left represent Stress Index (SI) scores of a sample of 20 high-level business executives. In the general population, this Stress Index is normally distributed and has a mean of 60.2 and a standard deviation of 27.1. Enter this data into SPSS.

· Generate descriptive statistics for this variable.

· Generate a histogram for this variable.

· In your data set, standardize the SI scores by transforming them into z-scores

· SPSS will automatically name the new variable.

· Which z-scores corresponds to a raw SI score of 60, 104, and 184?

· Does the distribution reflect the distribution in the general population?

· Support your answer.

1-a)

Generate descriptive statistics for this variable.

Answer: Descriptive Statistics Table

1-b)

Generate a histogram for this variable.

Answer: Histogram

1-c)

In your data set, standardize the SI scores by transforming them into z-scores under a new variable “ZSI.” Using your data set as a reference, what z-score corresponds to a raw SI score of 60?

To a raw SI score of 104? To a raw SI score of 184?

60

Answer

104

Answer

184

Answer

1-d)

Based on what you have been told about SI scores in the beginning of the problem,

does this sample’s distribution seem to reflect the distribution of SI scores in the general population?

Why or why not?

Answer

Justification

Part IV: Cumulative

Data provided below for respective questions.

Part IV: Question 1a-1d (Non-SPSS)

A counselor wants to find out whether adding a Bible study component to treatment leads to different scores on a measure of generalized anxiety as compared to treatment without a Bible study component.

He assigns clents to 1 of 2 groups:

Group 1 participates in treatment plus a Bible study component.

Group 2 participates in standard treatment without the Bible study component.

1-a)

What is the independent variable in this experiment?

Answer

1-b)

What is the dependent variable?

Answer

1-c)

What is the likely null hypothesis for this experiment?

Answer

1-d)

What is the likely research hypothesis for this experiment?

Answer

Diagnosis

Narcissism

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

33

12

20

26

27

9

17

27

34

32

12

8

18

12

6

5

8

14

10

6

Part IV: Questions 2a & 2b (SPSS)

A forensic psychologist wants to examine the level of narcissistic personality traits in those who are diagnosed with antisocial personality disorder (ASPD) and those who do not qualify for ASPD within a local prison population. She administers a measure of narcissistic personality traits where higher scores indicate higher levels of narcissism and scores range from 0–35.

· Create a new SPSS data file for these scores.

· Name your variables in Variable View. Assign values to the “Diagnosis” variable as follows: 1 = ASPD; 2 = no ASPD

· Be sure to assign the correct level of measurement to each variable in the “Measure” column. Then return to Data View to enter the data.

· Compute descriptive statistics by diagnosis (that is, for each of the two groups in one table) using similar steps to those covered in Green and Salkind’s Lesson 21, Section 4 and in the Module 3 SPSS presentation (“High School GPA scores by Gender”).

· Construct a boxplot to show the difference between the 2 groups

2-a)

Compute descriptive statistics by diagnosis (that is, for each of the two groups in one table) (2 pts)

Answer: SPSS Table- Descriptive Statistics for Score (level of narcissistic personality) grouped by Diagnosis (ASPD/No ASPD):

[Paste one table]

2-b)

Construct a boxplot to show the difference between the scores of the 2 groups. (3 pts)

Answer: Boxplot

Submit Homework 5 by 11:59 p.m. (ET) on Monday of Module/Week 5. Remember to name file appropriately.

Done!

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