Unit 4 Assignment 1 Answer Template

Unit 4 Assignment 1 Answer Template1unit 4 Assignment 1

The assignment involves analyzing z scores in SPSS, understanding Type I and Type II errors through case studies, and interpreting null hypothesis testing results. The task requires extracting statistical output from SPSS, performing calculations, and providing scholarly explanations in complete sentences following APA guidelines.

Paper For Above instruction

In the realm of statistical analysis, understanding how to accurately interpret z scores, Type I and Type II errors, and null hypothesis testing is fundamental. This paper provides a comprehensive examination of these concepts through practical application in SPSS and case study analysis, emphasizing their significance in research decision-making.

Section 1: z Scores in SPSS

Z scores are standardized scores that indicate how many standard deviations a data point (X) is from the mean (M). They are particularly useful when population parameters are unknown, and sample data is used for estimation. To calculate z scores in SPSS, the software's Descriptive Statistics function is employed on the dataset grades.sav. After selecting the total variable and opting to save standardized values, SPSS produces a new variable, Ztotal, that contains the z scores for each case.

To interpret the data, first, the sample mean (M) and standard deviation (s) are determined from the output. Suppose SPSS reports M=78.5 and s=10.2 for the total scores. These values are foundational for subsequent calculations. For example, to compute the z score for Case #53 with an unstandardized score (X) of 85, the formula (X - M) / s is used, resulting in (85 - 78.5) / 10.2 ≈ 0.65, which indicates that this case's score is approximately 0.65 standard deviations above the mean.

Running Descriptives on the Ztotal variable reveals a mean close to 0 and a standard deviation of approximately 1, which are expected properties of standardized scores. For instance, if the output shows a mean of 0.02 and a standard deviation of 1.01, it confirms the proper standardization process. A z score of 1.51, as found for Case #6, signifies that the score is 1.51 standard deviations above the mean, corresponding to roughly the 93rd percentile, indicating a fairly high score in the distribution.

The case with the lowest z score can be identified by locating the minimum value in Ztotal. Assuming this is -2.05, the corresponding percentile rank is approximately the 2nd percentile, which indicates that this score is among the lowest in the distribution. Conversely, the highest z score, say 2.10, falls near the 98th percentile, suggesting it is an outstandingly high score.

Section 2: Cases Studies of Type I and Type II Errors

A Type I error occurs when a researcher incorrectly rejects the null hypothesis when it is actually true. Applied to a jury setting, a correct decision would be finding the defendant not guilty when innocent or guilty when guilty. A Type I error would involve convicting an innocent defendant (wrongly rejecting the null hypothesis of innocence), while a correct decision involves acquitting a guilty defendant.

In the context of organizational research, a Type I error might involve incorrectly concluding that job satisfaction is related to organizational citizenship behavior when it is not. This error is influenced by the significance level (alpha), which determines the threshold for rejecting the null hypothesis. Setting alpha at 0.05 means there is a 5% risk of committing a Type I error. A researcher concerned about this risk might choose a more conservative alpha, thereby reducing the chance of false positives but increasing the risk of Type II errors—failing to detect a true effect.

In clinical trials, particularly when testing a new antidepressant, a Type I error would imply concluding the drug is effective when it actually is not. To minimize this risk, the researcher can employ stringent significance criteria (e.g., p

Section 3: Case Studies of Null Hypothesis Testing

When analyzing p values from SPSS tests, decisions about rejecting the null hypothesis depend on predetermined alpha levels, typically 0.05. For example, with p = 0.07 in a group difference test, the p value exceeds 0.05, leading to a failure to reject the null hypothesis; thus, no significant difference is detected. Conversely, a p value of .001 indicates strong evidence against the null, and the null would be rejected, implying significant group differences.

For the tests with p values of .07, .50, and .001, the conclusions are as follows: the first does not reject the null, suggesting no significant group difference; the second also fails to reject, indicating an insignificant association; the third rejects the null, showing significant differences. It is crucial to interpret these results in the context of effect sizes and practical significance beyond mere statistical significance.

If a researcher calculates a p value of .86 and erroneously rejects the null hypothesis, this constitutes a Type I error, because the high p value indicates weak evidence against the null, and rejecting it is inappropriate. This mistake could lead to false claims about effects or differences that do not truly exist, emphasizing the importance of adhering to the significance threshold and understanding p values' implications.

Explaining the phrase “p less than .05” involves clarifying that this criterion determines the likelihood of observing the data if the null hypothesis is true. Specifically, it means that the probability of obtaining the observed results, or more extreme, under the null is less than 5%. If this condition is met, researchers typically reject the null hypothesis, considering the findings statistically significant.

References

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  • Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). SAGE Publications.
  • Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences (10th ed.). Cengage Learning.
  • Hancock, G. R., & Mueller, R. O. (2010). Structural equation modeling: A second course. IAP Academic Publishing.
  • Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Sage.
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  • Meyers, L. S., Gamst, G., & Guarino, A. J. (2013). Applied multivariate research. Sage Publications.
  • Field, A., Miles, J., & Field, Z. (2012). Discovering statistics using R. SAGE Publications.
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