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401077 Introduction to Biostatistics For Sample Size Calculations

For this part of the assignment the research article provide is “Transport behaviours among older teenagers from semi-rural New Zealand” by Ward et al., (2015) published in Australian and New Zealand journal of public health. For analysing the paper Strobe Checklist for reporting of clinical observational studies is used as the basis.

Answer:

The sample size for the research is presented ambiguously by the researchers. The researchers though have informed that the study participants are from 12 secondary schools, 8 with in-class and 4 at-home participants. However, the researchers did not mention the number of in-class and at-home students. Moreover, the information for the number of male and female students for both the study modes have not been given. The researchers have only delivered the total number of study participants and also the number of male and female participants.  

Hence, it can be concluded that the sample size calculations have not been adequately addressed.

Item 12

In the present study the total number of students using a particular mode of transport in the last month has been presented as a frequency and percentage of the total number of study participants. Further, the frequency and percentage of transport frustration in last month as well as their licensing position are also presented. However, the researchers have presented the sample size of males and females using transport mode, frustration in last month and licensing in a highly ambiguous manner.

Further the statistical method used for the analysis of the data – Chi-square test has not been presented in a very clean manner.  

No explanation was provided about any missing data.

Hence, it can be concluded that the statistical methods for the research have not been adequately addressed.

Item 13

The research paper by Ward et al., never mentioned the total number of students in the 12 schools. Moreover, the total number of in-class and at-home students were never mentioned. The researchers have only informed that the overall response rate is 71.5% (or 775 students). Further, they have added that the response rate for in-class survey was 77.2% and for at-home was 65.6%. In addition, while the researchers have described that the male and female responses were 62.3% and 37.7% respectively, they did not provide information on the number of males and female in-class students.

Thus, it can be concluded from the study on the participants was poorly addressed as should reported according to STROBE’s 13a.

Moreover, the reasons for non-participation in the research was also not addressed. Thus section 13b of STROBE’s statement was also not addressed.   

Item 14

Table 1 of the research article clearly presents the frequency and percentages of gender, age, area, ethnicity and self-reported income of the students. Extending the study further in table 2, the researchers present the frequency and percentage of transport mode and frustration mode in the last month of the participants. The count and percentage of licensing characteristics of the students have also been addressed. Further, the transport and frustration mode and licensing has also been segregated according to percentage of females and males.  

Thus the STROBE statement for item 14a has been well addressed.  

Missing data was included in the analysis.

Thus the STROBE statement for item 14b has been well addressed.  

Item 15

The study can be classified as a cross-sectional study. The transport behaviour amongst male and female students were compared using Chi-square test. The results are not presented in a tabular form. However, the study finds that significant differences exists between the two sexes for transport mode, transport frustration and licensing

Item 15c of Strobe’s Statement is well addressed.

Item 16

Neither Unadjusted estimates nor confounder estimates were used in the study. Moreover, confidence intervals were also not calculated.

Thus, Item 16 of the Strobe’s Statement is not addressed.

Item 17

Transport differences in subgroups regarding age-groups, weekly income, ethnicity were not discussed.

Thus, Item 17 of the Strobe’s Statement is not addressed.

Question 2: Note: Students will get different answers as the data sets differ.

For this part of the assignment data set taken is datafor19151436. The aim is to predict self-reported sedentary hours per week of 17-year residents of NSW from the number of activities attended in the past month. Further, the research wants the prediction based on gender.

From the analysis of the data set it is found that the sample size of the study is 271. 48.34% or 131 residents were females and 51.66% or 140 were males.

Table 1: Frequency Distribution of Sex of the residents

Sex

Frequency

Percentage

Female

131

48.34%

Males

140

51.66%

Figure 1: Distribution of Sex

Table 2: Descriptive Statistics for Activities and sed

Statistics

Activities

sed

Mean

7.199262

10.699262

sd

2.307187

3.133771

Minimum

1.0

3.7

Maximum

13.0

21.1

1st Quartile

5.00

8.35

3rd Quartile

9.00

12.85

Median

7.00

10.3

IQR

4.0

4.5

The average number of activities attended by the residents is 7.199262 with a standard deviation of 2.307187. The minimum and maximum number of activities attended by the residents are 1.0 and 13.0 respectively. The median number of activities attended is 7.00.  

The average number of sedentary hours per week for the residents is 10.699262 with a standard deviation of 3.133771. The minimum and maximum sedentary hours of the residents are 3.7 and 21.1 hours respectively. The median sedentary hours of the residents is 4.50. 

The number of hours of activities of the residents is normally distributed.  

The number of sedentary hours of the residents seems to be right skewed.

Table 3: 95% Confidence Interval

 

Activities

sed

Lower Limit

6.923333

10.32448

Upper Limit

7.475191

11.07405

The 95% CI of number of activities attended in the past month is 6.82333 and 7.475191.

The 95% CI of hours of sedentary hours of the residents is 10.32448 and 11.07405.

To predict Sed from activities correcting for sex linear regression is used. Sex is factorised as female = 0 and male = 1.

The regression model is

 

Estimate

Std. Error

t-value

Pr

Intercept

21.68057

0.71964

30.127

<2e-16

Activities

-1.29016

0.07877

-16.379

<2e-16

Sex(T.male)

-3.27737

0.36300

-9.029

<2e-16

Thus the model is

Sed = 21.68057 – 1.29016*activities – 3.27737*sex

Where female = 0 and male = 1.

From the above it equation it can be inferred that with increase in activities attended in the past month there is a decrease in self-reported sedentary hours per week.

Thus sed for female = 21.68057 – 1.29016*activities

Sed for male = 18.4032 -  – 1.29016*activities

Further, it can also be inferred that with similar increase in activities in the past month the self-reported sedentary hours for males is lower than females.

The coefficients of activities and sex are statistically significant at 0.01 level of significance.

Moreover, 50.69% of sed can be predicted from activities while correcting for sex.  

The analysis of the dataset shows that there are more males than females in the dataset. Moreover, it is found that the number of activities attended by the residents in the past month is normally distributed. However, the self-reported sedentary hours per week of the residents is skewed.

Further, it is found that we can predict self-reported sedentary hours per week of the residents from activities attended in the past month with the addition of sex. Moreover, the self-reported sedentary hours per week is less for males than for females for activities in the past month for both males and females.   

References

Ward, A. L., McGee, R., Freeman, C., Gendall, P. J., & Cameron, C. (2018). Transport behaviours among older teenagers from semi?rural New Zealand. Australian and New Zealand journal of public health, 42(4), 340-346.

Vandenbroucke, J. P., Von Elm, E., Altman, D. G., Gøtzsche, P. C., Mulrow, C. D., Pocock, S. J., ... & Egger, M. (2007). Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): explanation and elaboration. Annals of internal medicine, 147(8), W-163.

Von Elm, E., Altman, D. G., Egger, M., Pocock, S. J., Gøtzsche, P. C., Vandenbroucke, J. P., & Strobe Initiative. (2007). The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies. Preventive medicine, 45(4), 247-251.

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