UNIT 3: Written Assignment

HS 4241 - 01 Psychopathology and Mental Health - UNIT 3 Written Assignment Instructor: Pankaj Mehrotra Date: 15/02/2025 QUESTION 1 Bayes' Theorem states that: We are given the following probabilities: ● P(A∣B)=0.35 (Probability of having condition A given condition B) ● P(A)=0.4 (Prior probability of condition A) ● P(B)=0.10 (Prior probability of condition B) Now, applying Bayes’ Theorem: P(B∣A)= (0.35×0.10) / 0.4 → P(B∣A)=0.0875 Therefore, if one has condition A, the likelihood of having condition B is 0.0875, or 8.75 percent. QUESTION 2 Step 1: Define Key Terms ●​ Sensitivity: The probability that a test correctly identifies those with the disease (P(T+∣D+)). ●​ Specificity: The probability that a test correctly identifies those without the disease (P(T−∣D−)). ●​ Positive Predictive Value (PPV): The probability that a person who tests positive actually has the disease (P(D+∣T+)). Step 2: Organize Given Data ●​ Total subjects tested = 1500 ●​ Positive test results = 250 ●​ True positives (Actual disease cases among positives) = 110 ●​ False positives (Tested positive but do not have disease) = 250−110=140 ●​ False negatives (Tested negative but later developed disease) = 20 ●​ Total actual disease cases = 110+20=130 ●​ Total true negatives = 1500−130−140=1230 Step 3: Calculate Sensitivity, Specificity, and PPV 1. Sensitivity Sensitivity = True Positives / Total with Disease = 110 / 130​= 0.846 or 84.6% 2. Specificity Specificity= True Negatives / Total without Disease = 1230/ 1370 = 0.898 or 89.8% 3. Positive Predictive Value (PPV) PPV= True Positives / Total Positive Tests = 110 / 250 = 0.44 or 44.0% Step 4: Examine the Details A 75% test specificity indicates that 75% of those without the illness are properly identified by the test. But it also means that 25% of people who don't have the condition get a false positive, which means they are mistakenly diagnosed with it. Step 5: Do You Think This Test Would Be Good? The test is effective at identifying real illness patients because of its comparatively high sensitivity (84.6%). Strong specificity (89.8%) suggests a low rate of false positives. The PPV is only 44%, though, which indicates that over half of people who test positive do not genuinely have the illness. The results of false positives and false negatives will determine whether or not this test should be used: High sensitivity makes the test beneficial if false negatives (missed instances) are harmful (e.g., life-threatening sickness). Low PPV is an issue if false positives result in needless worry or expensive follow-up testing. Suggestion: Although this test is helpful for initial screening, confirmatory testing—such as a more specific test—is required before diagnosing or treating individuals because of the low PPV. QUESTION 3 Design of the Experiment: Examining the Impact of Sleep on Academic Achievement Objective: to investigate the relationship between students' academic performance and sleep length. Methodology: Participants: 200 college students chosen at random. Data collection: At the conclusion of the week, participants will complete a standardized academic test and indicate how much sleep they typically get. Survey Components: Details about the demographics (age, gender, major) Duration of sleep (self-reported) Academic achievement as measured by test results Testing Reliability in the Study 1. Internal Consistency (Are the survey items measuring the same concept?) Numerous questions about sleep habits (such as bedtime, wake-up time, and naps) will be included in the questionnaire. Testing: To determine whether answers to these questions are correlated and reliably gauge sleep habits, use Cronbach's alpha. Good internal consistency is indicated by a high Cronbach's alpha (> 0.7). 2. Stability (Test-Retest Reliability) (Are the results consistent over time?) The sleep survey will be completed by participants twice: once at the beginning of the study and again at its conclusion. Testing: Use Pearson's correlation to compare the answers from the two surveys. Stable reactions throughout time are indicated by a significant correlation (around 1). 3. Interrater Reliability (Do different researchers record data consistently?) If the academic test is graded by more than one researcher, we will compare their results for the same set of answers. Testing: To evaluate rater agreement, use the Intraclass Correlation Coefficient (ICC) or Cohen's kappa. Strong dependability is indicated by high values (> 0.75). Conclusion: By addressing interrater reliability, stability, and internal consistency, we make sure that our study yields reliable and consistent data, enhancing the validity of inferences made between academic performance and sleep. QUESTION 4 With a Cohen's Kappa of 0.85, the raters' agreement is much higher than would be predicted by chance. This implies that the ratings are quite trustworthy and that raters are regularly assigning comparable scores or classifications to the data. A Kappa value above 0.80 is regarded as outstanding in research, indicating a reliable and consistent measurement procedure. REFERENCES: ●​ Illowsky, B. and Dean, S. (2017). Introductory Statistics. OpenStax Rice University. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Retrieved from https://my.uopeople.edu/pluginfile.php/1954716/mod_page/content/3/TEXT%20intro ductory-statistics.compressed.pdf ●​ Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46. https://doi.org/10.1177/001316446002000104 ●​ Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334. https://doi.org/10.1007/BF02310555 ●​ McHugh, M. L. (2012). Interrater reliability: The kappa statistic. Biochemia Medica, 22(3), 276–282. https://doi.org/10.11613/BM.2012.031 ●​ Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). McGraw-Hill. ●​ Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420–428. https://doi.org/10.1037/0033-2909.86.2.420