Biostatistics Assignment Sample Using GHQ-12 Data Qustion Answer

Statistical Analysis of Mental Health Survey Data

Q.1: Classify the variables name, sex, age, birth country, and exercise frequency according to their level of measurement and state the appropriate statistical methods for each.

Answer: Name In this variable, there is a classification. Names are not ordered in any particular way; they are labels and are classified accordingly. The name of each person is a label, a different label, but it says nothing of a hierarchical relationship between them or a quantitative one.

Sex: This is a binary variable = It has two and only two possible values. It is a binary variable because it can only have 2 options for instance Male (M) and Female (F). This sort of variable is the simplest type of categorical variable; and it divides the data into two clearly distinct categories.

Years of age: This is a continuous variable. Since age is a continuous variable it can be precisely measured and it can attain any value within the given range (for instance 45, 45. 5). Many kinds of analyses can be done with continuous variables, for instance, computation of means and variances.

Birth country: This is a type that changes category. It splits people based on geographic origin, based on the country they were born in. The categories are all exclusive; there is no prescribed quantitative correlation between them.

Exercise frequency: This is an ordinal variable the values taken by this variable are labelled and referred to by ordinal numbers hence the name ordinal variable (Pagano, Gauvreau, & Mattie, 2022). It formats the workout frequency in a rational way. These categories are not of equal distance one from the other, which determines the choices of statistics even though it produces a ranking of exercise routines.

These classifications should however be understood so as to settle on the correct statistical analyses. Categorical and dichotomous variables are mostly analyzed using frequency distributions and chi-square tests. These tools are useful in finding out co-relation between the various categories (Gustafsson & Nilsson, 2022). For the analysis of interval /ratio level data descriptive statistics such as mean and standard deviation are used to check for central tendency while the measure of variation such as standard deviation is used to check on dispersion.

Q.2: Using summary statistics and graphical displays, compare the GHQ-12 scores of migrants and refugees and comment on differences in mental health outcomes.

Answer:Figure 1: Summary statistics for GHQ12 by mig_typ

(Source: Self-created in Rstudio)

Figure 2: Histogram

(Source: Self-created in Rstudio)

Figure 3: Density plot

(Source: Self-created in Rstudio)

Figure 4: Density plot

(Source: Self-created in Rstudio)

The scores obtained in the GHQ12 are compared, and there are differences and similarities in the results of the migrants and refugees surveyed. Averaging 19. 07 and 17. 2, and 1 respectively although this can vary greatly with medians of 19. 00 and 17. First of all, the refugee group results in slightly higher GHQ12 scores than the migrant group does. This points to the fact that the general health status of migrants is perceived to be better than the refugees’ (Chowdhry, 2023). Interestingly, the distribution of scores is almost similar when the refugee score was compared to that of migrants although the measure of central tendency is higher in the former group; refugees' mean score was 7. 39 while for the migrants it was 6. 92.

Q.3: Using a scatter plot and correlation coefficient, describe the strength and direction of the relationship between GHQ-12 and PHQ-4 scores.

Answer:Figure 5: Scatter plot

(Source: Self-created in Rstudio)

A positive correlation between the studied parameters, namely General Health Questionnaire (GHQ 12) and Patient Health Questionnaire (PHQ 4) indices is confirmed by the present work. This is graphically reflected by the scatterplot in which one sees that PHQ4 rises with GHQ12, though not as steeply. To suggest that the positive direction of this association is greater scores on one questionnaire means greater scores on the other. This is further buttressed by the fact that the nature of the relationship between the two variables is strongly positively indicated by the correlation coefficient of r=0. 54 which indicates a high correlation between GHQ12 and PHQ4 scores. However, there is a lot of divergence, despite the fact that the correlation between the variables is clearly evident; this is only natural (Rossi, 2022). Larger scores in both tools may signify poorer mental health linkages since, judging from the nature of the data points rising on an ascending order, it is most likely that both GHQ12 and PHQ4 are measuring congruent parameters of mental health.

Q.4: Using a cross-tabulation of NESB status and housing status, interpret the association and calculate the relevant conditional probabilities.

Answer:Figure 6: Cross tabulation

(Source: Self-created in Rstudio)

Figure 7: Cross-tabulation with row percentages

(Source: Self-created in Rstudio)

1. a) In the present study, R studio was used to develop cross-tabulation that explained the existing relationship. The numbers of people in each group with housing status satisfactory and unsatisfactory are presented in the following table. To show the rate at which NESB and non-NESB people take each housing status, row percentages were computed (Reeder, Banks, & Holubkov, 2021). By the help of the cross tabulation the distribution of NESB status across the various housing statuses shows that it is possible to reveal any existing connections between these factors clearly.
2. b) The likelihood of choosing at random from among NESB individuals who have enough housing is 0.
3. c) Chance of inadequate housing for an individual chosen at random from NESB, this is not possible at all.

Q.5: Calculate probabilities related to the selection of migrants from a population and evaluate whether binomial distribution assumptions are satisfied, justifying the appropriate probability model.

Answer:Figure 8: analysis result

(Source: Self-created in Rstudio)

1. a) The probability of misleading memory is, overall, 0.2073 probability or 20. 73% of selecting exactly two migrants among eight persons picked at random. It is possible to view this as the chance, which is equal to 1 in 5, that one observes exactly 2 migrants when randomly selecting 8 individuals from within this population subset.
2. b) If the four people in the box represent eight people randomly selected from the population what are the probabilities are 0.9492. Only 94% probability of selecting not more than five migrants. That is why for any non-systematic arriving group of eight individuals, it can be confidently stated that there will be no more than five migrants among them.
3. c) When analysing the assumptions made relating to probabilities necessary for selection of persons from a given population, one finds that some of these are met, whereas others are not. To fulfil the number of trials prerequisite as selecting a specific number of eight participants, satisfies this prerequisite (Hirsch, 2021). Likewise, because each person belongs to one of the two groups, migrants or refugees there is a clear assumption that there are only two possibilities. However, random sampling without replacement of a population of 605 persons means that each choice alters the probability of subsequent choices greatly and therefore, the assumption of independence is very likely to be violated. This interdependence can be assumed to have an effect on how good the probabilities are estimated. If the data represents a random sample from the population, an assumption of equal probability of success is met; however, this assumption may also be compromised in the sample if there exists inherent patterns or clusters (Oliveira, 2020). Hypergeometric distribution rather than a binomial distribution should be used to correct for sampling without replacement owing to the violation of independence on the grounds that if more people were to be picked then this makes much more sense.

Q.6: Assuming GHQ-12 scores follow a Normal distribution, calculate (i) the probability of a score exceeding 24 and (ii) the cut-off value for the top 10% of scores.

Answer:Figure 9: analysis result

(Source: Self-created in Rstudio)

The Normal distribution parameters for GHQ12 scores with a mean of 18.12 and a standard deviation of 7.31.

1. a) Approximately 0.21, or 21% is the score which is greater than the 24 for the probability that a randomly selected participant has a GHQ12.
2. b) The expectation is at least 10% of participants have a GHQ12 score higher than a certain value, the threshold score would be approximately 27.48. This means the top 10% of scores start from this value.

Q.7: Using the Central Limit Theorem, determine probabilities and percentile cut-offs for the sampling distribution of the mean GHQ-12 score.

Answer:

• Due to the fact that each GHQ12 score is independently derived from a Normal distribution with parameters μ = 18 and σ = 7 a Normal distribution is also observed for the sampling distribution of the sample means from 88 data sets. That is why there is a Central Limit Theorem. In this sampling distribution μ=18 which will be equal to the population mean. The standard error is derived from the formula σmean = σ/√n where ‘σmean’ represents the standard deviation of the sample means (Sullivan, 2022). The sample size is defined by n; if the actual number of data points used in each set is not indicated, the standard error is equal to σmean = 7/ √5 ≈ 3. 13.
• Based on the z-score for the Normal distribution is the probability that the sample mean of GHQ12 score for one of the 88 data sets is greater than 24.

Z = (X -μ)/σmean = (24-18)/3. 13 ≈ 1. 92

Thus, by either your calculator or a standard set of Normal distribution tables, the probability of a z-score of 1. 92 is roughly 0. 0274. A probability of 74% is equivalent to 0.74; of course this is approximate since it is rounded off.

3. It is often necessary to get the 90-percentile of the Normal distribution as regards mean, equal to 18 and standard error equal to 3. 13 so that the threshold, representing the sample mean of the GHQ12 in the top 10% could be determined (Mishra & Khan, 2024). About 1. The z-score for the ninth decile is 28. Applying this z-score:

X = μ + z * σmean = 18 + 1. 28 * 3. 13 = 21. 02

Consequently, it can be expected that in a sampling distribution of at least 10% of the individual sample means are larger than approximately 21. 02.

Reference list

Journals

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Pagano, M., Gauvreau, K., & Mattie, H. (2022). Principles of biostatistics. Chapman and Hall/CRC. Retrieve from: https://academic.oup.com/jrsssa/article-abstract/186/4/897/7105840 Retrieve on: [7.8.24].

Chowdhry, A. K. (2023). Principles of Biostatistics. Retrieve from:  Retrieve on: [7.8.24].

Rossi, R. J. (2022). Applied biostatistics for the health sciences. John Wiley & Sons. Retrieve from: https://books.google.com/books?hl=en&lr=&id=88l6EAAAQBAJ&oi=fnd&pg=PR5&dq=Introduction+to+Biostatistics&ots=o5qh_6CLvn&sig=PEv1osLGMuDvBnb3sEe1H0uer80 Retrieve on: [7.8.24].

Hirsch, R. P. (2021). Introduction to biostatistical applications in health research with Microsoft Office Excel and R. John Wiley & Sons. Retrieve from: https://books.google.com/books?hl=en&lr=&id=6OMXEAAAQBAJ&oi=fnd&pg=PR13&dq=Introduction+to+Biostatistics&ots=ltHyaPPwcx&sig=62Pn1XF72tmRoj_vbrKEKwR4NCk Retrieve on: [7.8.24].

Oliveira, A. G. (2020). Biostatistics decoded. John Wiley & Sons. Retrieve from: https://books.google.com/books?hl=en&lr=&id=EN_7DwAAQBAJ&oi=fnd&pg=PR11&dq=Introduction+to+Biostatistics&ots=N-wmIT6uz9&sig=_e7F-iRpT0An3C2EYWlcjvsfQN8 Retrieve on: [7.8.24].

Sullivan, L. M. (2022). Essentials of biostatistics for public health. Jones & Bartlett Learning. Retrieve from: https://books.google.com/books?hl=en&lr=&id=vHN4EAAAQBAJ&oi=fnd&pg=PP1&dq=Introduction+to+Biostatistics&ots=UTBuNPfq6N&sig=cfVtuOBrg9CrCL6NqgADMw5N3q0 Retrieve on: [7.8.24].

Mishra, A., & Khan, M. M. (2024). The science and art of biostatistics: a comprehensive overview. Asian Journal of Hospital Pharmacy, 45-51. Retrieve from: https://www.ajhponline.com/index.php/journal/article/view/86 Retrieve on: [7.8.24].

Reeder, R. W., Banks, R., & Holubkov, R. (2021). Biostatistics and Evaluating Published Studies. Pediatric Critical Care: Text and Study Guide, 1569-1593. Retrieve from: https://link.springer.com/chapter/10.1007/978-3-030-53363-2_51 Retrieve on: [7.8.24].