Description
z Scores, Type I and II Errors, Hypothesis Testing
Running head: UNIT 4 ASSIGNMENT 1
1
Unit 4 Assignment 1
Sofia Matrosova-Khalil
Capella University
ED7864
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
2
Unit 4 Assignment 1
1. z scores in SPSS.
2. Case studies of Type I and Type II errors.
3. Case studies of null hypothesis testing.
Additional notes:
•
Answer in complete sentences.
•
Follow APA rules for scholarly writing.
•
Include a reference list if necessary.
•
Save your answers and upload this template to the assignment area for grading.
Section 1: z Scores in SPSS
A z score is typically analyzed when population mean (µ) and population standard
deviation (σ) are known. However, in SPSS, we can still calculate z scores with the grades.sav
data using the sample mean (M) and sample standard deviation (s). To do this, open grades.sav
in SPSS. On the Analyze menu, point to Descriptive Statistics, and then click Descriptives…
You will be calculating and interpreting z scores for the total variable. In the
Descriptives dialog box, move the total variable into the Variable(s) box. Select the Save
standardized values as variables option and click OK.
SPSS provides descriptive statistics for total in the Output window. SPSS also creates a
new variable in the far right column, labeled Ztotal, in the Data Editor area. Ztotal provides a z
score for each case on the total variable. You are now prepared to answer the following Section
1 questions.
Question 1
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
3
What is the sample mean (M) and sample standard deviation (s) for total? You will use
these values in Question 2 below.
z scores in SPSS.
[DataSet1] C:UserssmatrDownloadsgrades (2).sav
Descriptive Statistics
N
Minimum
total
105
Valid N (listwise)
105
54
Maximum
123
Mean
100.09
Std. Deviation
13.427
The sample mean is 100.09=M and sample standard deviation for total is 13.427=s
Question 2
A z score for this sample is calculated as [(X – M) ÷ s]. Locate Case #53’s unstandardized
total score (X) in the Data Editor. In the formula below, replace X, M, s, and ? to show how the
z score in Ztotal is derived for Case #53.
(X – M ) ÷ s = ?
x-100.09)/13.427=Ztotal, -3.43226
Question 3
Run Descriptives… on Ztotal. What are the mean and standard deviation of Ztotal?
(Hint: “0E7” in SPSS is scientific notation for 0). Are the mean and standard deviation what you
would expect? Justify your answer.
DESCRIPTIVES VARIABLES=Ztotal
/SAVE
/STATISTICS=MEAN STDDEV MIN MAX.
Descriptive Statistics
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
N
Minimum
Zscore(total)
105
Valid N (listwise)
105
-3.43226
Maximum
1.70655
4
Mean
.0000000
Std. Deviation
1.00000000
The mean is .0000000-M or 0. The standard deviation of Ztotal is 1.00000000=s or 1.
Question 4
Case number 6 has a Ztotal score of 1.56. What does a z value of 1.56 represent?
[Answer here in complete sentences.]
Question 5
Identify the case with the lowest z score. Refer to Appendix A in the Warner (2013) text.
Interpret the percentile rank of this z score rounded to whole numbers.
[Answer here in complete sentences.]
Question 6
Identify the case with the highest z score. Refer to Appendix A in the Warner (2013) text.
Interpret the percentile rank of this z score rounded to whole numbers.
[Answer here in complete sentences.]
Section 2: Cases Studies of Type I and Type II Errors
Question 7
A jury must determine the guilt of a criminal defendant (not guilty, guilty). Identify how
the jury would make a correct decision. Analyze how the jury would commit a Type I error
versus a Type II error.
[Answer here in complete sentences.]
Question 8
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
5
An I/O psychologist asks employees to complete surveys measuring job satisfaction and
organizational citizenship behavior. She intends to measure the strength of association between
these two variables. The researcher is concerned that she will commit a Type I error. What
research decision influences the magnitude of risk of a Type I error in her study?
[Answer here in complete sentences]
Question 9
A clinical psychologist is studying the efficacy of a new drug medication for depression.
The study includes a placebo group (no medication) versus a treatment group (new medication).
He then measures the differences in depressive symptoms across the two groups.
What would a Type I error represent within the context of his study? How can he reduce
the risk of committing a Type I error? How does this decision affect the risk of committing a
Type II error?
[Answer here in complete sentences.]
Section 3: Case Studies of Null Hypothesis Testing
Question 10
You are running a series of statistical tests in SPSS using the standard criterion for
rejecting a null hypothesis. You obtain the following p values.
Test 1 calculates group differences with a p value = .07.
Test 2 calculates the strength of association between two variables with a p value = .50.
Test 3 calculates group differences with a p value = .001.
For each test below, state whether or not you reject the null hypothesis. For each test, also
explain what your decision implies in terms of group differences (Test 1 and Test 3) and in terms
of the strength of association between two variables (Test 2).
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
Test 1 (group differences) =
Test 2 (strength of association) =
Test 3 (group differences) =
Question 11
A researcher calculates a statistical test and obtains a p value of .86. He decides to reject
the null hypothesis. Is this decision correct, or has he committed a Type I or Type II error?
Explain your answer.
[Answer here in complete sentences]
Question 12
You are proposing a research study that you would like to conduct while attending
Capella University. During the proposal, a committee member asks you to explain in your own
words what you meant by saying “p less than .05.” Provide an explanation.
[Answer here in complete sentences]
6
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
7
References
Provide references if necessary. This concludes Unit 4 Assignment 1. Save your answers
and upload this template to the assignment area.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd
ed.). Thousand Oaks, CA: Sage.
Purchase answer to see full
attachment
1
Unit 4 Assignment 1
Sofia Matrosova-Khalil
Capella University
ED7864
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
2
Unit 4 Assignment 1
1. z scores in SPSS.
2. Case studies of Type I and Type II errors.
3. Case studies of null hypothesis testing.
Additional notes:
•
Answer in complete sentences.
•
Follow APA rules for scholarly writing.
•
Include a reference list if necessary.
•
Save your answers and upload this template to the assignment area for grading.
Section 1: z Scores in SPSS
A z score is typically analyzed when population mean (µ) and population standard
deviation (σ) are known. However, in SPSS, we can still calculate z scores with the grades.sav
data using the sample mean (M) and sample standard deviation (s). To do this, open grades.sav
in SPSS. On the Analyze menu, point to Descriptive Statistics, and then click Descriptives…
You will be calculating and interpreting z scores for the total variable. In the
Descriptives dialog box, move the total variable into the Variable(s) box. Select the Save
standardized values as variables option and click OK.
SPSS provides descriptive statistics for total in the Output window. SPSS also creates a
new variable in the far right column, labeled Ztotal, in the Data Editor area. Ztotal provides a z
score for each case on the total variable. You are now prepared to answer the following Section
1 questions.
Question 1
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
3
What is the sample mean (M) and sample standard deviation (s) for total? You will use
these values in Question 2 below.
z scores in SPSS.
[DataSet1] C:UserssmatrDownloadsgrades (2).sav
Descriptive Statistics
N
Minimum
total
105
Valid N (listwise)
105
54
Maximum
123
Mean
100.09
Std. Deviation
13.427
The sample mean is 100.09=M and sample standard deviation for total is 13.427=s
Question 2
A z score for this sample is calculated as [(X – M) ÷ s]. Locate Case #53’s unstandardized
total score (X) in the Data Editor. In the formula below, replace X, M, s, and ? to show how the
z score in Ztotal is derived for Case #53.
(X – M ) ÷ s = ?
x-100.09)/13.427=Ztotal, -3.43226
Question 3
Run Descriptives… on Ztotal. What are the mean and standard deviation of Ztotal?
(Hint: “0E7” in SPSS is scientific notation for 0). Are the mean and standard deviation what you
would expect? Justify your answer.
DESCRIPTIVES VARIABLES=Ztotal
/SAVE
/STATISTICS=MEAN STDDEV MIN MAX.
Descriptive Statistics
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
N
Minimum
Zscore(total)
105
Valid N (listwise)
105
-3.43226
Maximum
1.70655
4
Mean
.0000000
Std. Deviation
1.00000000
The mean is .0000000-M or 0. The standard deviation of Ztotal is 1.00000000=s or 1.
Question 4
Case number 6 has a Ztotal score of 1.56. What does a z value of 1.56 represent?
[Answer here in complete sentences.]
Question 5
Identify the case with the lowest z score. Refer to Appendix A in the Warner (2013) text.
Interpret the percentile rank of this z score rounded to whole numbers.
[Answer here in complete sentences.]
Question 6
Identify the case with the highest z score. Refer to Appendix A in the Warner (2013) text.
Interpret the percentile rank of this z score rounded to whole numbers.
[Answer here in complete sentences.]
Section 2: Cases Studies of Type I and Type II Errors
Question 7
A jury must determine the guilt of a criminal defendant (not guilty, guilty). Identify how
the jury would make a correct decision. Analyze how the jury would commit a Type I error
versus a Type II error.
[Answer here in complete sentences.]
Question 8
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
5
An I/O psychologist asks employees to complete surveys measuring job satisfaction and
organizational citizenship behavior. She intends to measure the strength of association between
these two variables. The researcher is concerned that she will commit a Type I error. What
research decision influences the magnitude of risk of a Type I error in her study?
[Answer here in complete sentences]
Question 9
A clinical psychologist is studying the efficacy of a new drug medication for depression.
The study includes a placebo group (no medication) versus a treatment group (new medication).
He then measures the differences in depressive symptoms across the two groups.
What would a Type I error represent within the context of his study? How can he reduce
the risk of committing a Type I error? How does this decision affect the risk of committing a
Type II error?
[Answer here in complete sentences.]
Section 3: Case Studies of Null Hypothesis Testing
Question 10
You are running a series of statistical tests in SPSS using the standard criterion for
rejecting a null hypothesis. You obtain the following p values.
Test 1 calculates group differences with a p value = .07.
Test 2 calculates the strength of association between two variables with a p value = .50.
Test 3 calculates group differences with a p value = .001.
For each test below, state whether or not you reject the null hypothesis. For each test, also
explain what your decision implies in terms of group differences (Test 1 and Test 3) and in terms
of the strength of association between two variables (Test 2).
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
Test 1 (group differences) =
Test 2 (strength of association) =
Test 3 (group differences) =
Question 11
A researcher calculates a statistical test and obtains a p value of .86. He decides to reject
the null hypothesis. Is this decision correct, or has he committed a Type I or Type II error?
Explain your answer.
[Answer here in complete sentences]
Question 12
You are proposing a research study that you would like to conduct while attending
Capella University. During the proposal, a committee member asks you to explain in your own
words what you meant by saying “p less than .05.” Provide an explanation.
[Answer here in complete sentences]
6
UNIT 4 ASSIGNMENT 1 ANSWER TEMPLATE
7
References
Provide references if necessary. This concludes Unit 4 Assignment 1. Save your answers
and upload this template to the assignment area.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd
ed.). Thousand Oaks, CA: Sage.
Purchase answer to see full
attachment
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