# z Scores in SPSS

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A z value is normally evaluated when an average population (μ) and a standard population difference (β) are known. In SPSS, however, z values for grades.sav data can still be determined using a mean (M) and standard sample deviation (s). Open.sav in SPSS to do this. Select Summary Statistics and then Explanations from the Analyze menu.
The z scores for the total variable are measured and interpreted. Shift the total variable into the Variable(s) window, as seen on the next tab. Choose the Save as value option the uniform variables and click OK. SPSS provides descriptive statistics for total in the Output window. SPSS also creates a new variable in the far right column of the Data Editor area labeled Z total. Z total provides a z score for each case on the total variable. You are now prepared to answer the following Section 1 questions.
Cases Studies of Type I and Type II Errors
Question 1
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.
A Type I error occurs when the jury rejects a null hypothesis which is in fact real while a Type II error occurs when a null hypothesis presented is incorrect, but an individual fails to decline it. In order, for the jury to make a correct decision they would have to consider both types of errors i.e. Type I and Type II errors presented in the case. The jury may commit a Type I error but rejecting evidence which is in fact real. A type II error will be committed by the jury if they accept a deposition from a witness who is lying.
Question 2
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?
The magnitude of risk of Type I error in the study can result from the assumptions that will be made by the researcher. Assumptions in a research study are used to determine the final findings of a study. However, the risk magnitude of committing Type I error increases because the survey findings would be conflicting with the assumption hence the researcher may decide to reject these findings which are truthful.
Question 3
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?
In this study, a type I error would be represented by rejecting the findings that would suggest that the new medication would reduce depressive symptoms in the group being treated using the new drug. The psychologist can minimise the risk of committing a Type I error by following the results of the study and not assumptions made before the commencement of the survey. However, in reaching this decision, the psychologist risk committing a Type II by accepting the findings of the study which may have been tampered with hence accepting false results.
Section 3: Case Studies of Hypothesis Testing
Question 4
You are running a series of statistical tests in SPSS using the _x0093_standard_x0094_ 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).
Test #1 (group differences) = I accept the null hypothesis because the group difference of p value implies that the variables considered are from a wider group.
Test #2 (strength of association) = I reject the null hypothesis because the association value between the two variables with a p value is much higher than the value of the variables.
Test #3 (group differences) = I accept the null hypothesis because the value of p from the test is real.
Question 5
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.
The researcher commits a Type I error by rejecting the result of the test because the actual value of p is within the range of .86 hence the researcher rejects the null hypothesis which is correct.
Question 6
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 _x0093_p less than (<) .05._x0094_ Provide an explanation. The saying p less than (<) .05 means that the value of p when test are done should be any number provided it does not exceed .05. A value that exceeds .05 should therefore be rejected for being false.

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