Reference no: EM131223367

Question 1 -

Thirty teeth were randomly allocated into three groups of 10 and a cavity in each tooth filled using one of three preparations. Following immersion in a dye, the percentage of linear leakage occurring at the tooth/restoration interface in each tooth was determined. The results are stored in columns of the file data2_Q1.sav in which the first column contains the percentages of length of penetration (PLP) and the second column contains the preparation used.

a) Produce an analysis of variance (ANOVA) table to determine if there are differences between the preparations using PLP measurement.

b) Assess the validity of the ANOVA assumptions which require data to follow normal distribution.

c) For the PLP measurements, conduct Bonferroni correction with the post-hoc tests to determine where any differences between the preparations lie.

d) Perform Kruskal-Wallis tests for the PLP measurements. What is your conclusion?

e) Use pairwise Wilcoxon rank-sum tests (with Bonferroni correction) to determine where any differences between preparations lie.

f) Which analysis do you think is most appropriate here - ANOVA or a nonparametric approach?

Question 2 -

Researchers at Leeds University School of Dentistry want to know whether registering with a NHS dental practice or a private dental practice will make a difference in children's regular dental check-ups. Consider the table of data collected:

a) What is the proportion of children that have registered with a NHS dental practice?

b) What is the proportion of children that have registered with a private dental practice?

c) What is the proportion of children that have registered with a NHS dental practice in the group of regular check-ups?

d) What is the proportion of children that have registered with a NHS dental practice in the group of non-regular check-ups?

e) For the NHS Dental Practice, compare the regular check-up group with the non-regular check-up group. What is the absolute difference in the proportions between the two groups?

f) Is there an association between dental practice and regular check-ups? Performance a hypothesis and state your conclusion?

g) What is the relative risk of not having regular check-ups when registering with a private practice compared with registering with NHS?

h) What is the odds ratio of non-regular check-ups for private practice comparing with NHS?

Question 3 -

A study considered the effect of diet control over caries development in children. Of 30 children, 15 were randomly selected to receive controlled diet over 5 years (cases), and the other 15 formed a control group. Eight of the 15 in control group developed caries during this 5-year period, while 2 of the 15 children developed caries in the study group. The data are stored in the file data2_Q3.sav.

a) State the null hypothesis and alternative hypothesis.

b) Which test should we use?  Why?

c) Perform the test of your choice. What is your conclusion?

Question 4 -

A study identified 47 patients in need of two fillings. Subjects were then treated with one filling using material A and the other filling with material B. In order to compare the success rate between material A and B over two years, the data are collected and stored in the file data2_Q4.sav and shown in the contingency table below.

a) State the null hypothesis.

b) What test should we use?

c) Perform the test of your choice to determine if the proportion of success with material A is the same as material B in this matched-pairs study.

Question 5 -

The data file data2_Q5.sav contains information on the percentage of people who brush their teeth at least once a day and the percentage of people who have caries for a range of developed and developing countries.

a) Produce a scatter plot of teeth-brush rate against percentage of caries and comment on the results.

b) Calculate Pearson's correlation coefficient for these data. Test whether the correlation coefficient is significantly different from zero.

c) Calculate Spearman's rank correlation coefficient for these data. Test whether the correlation coefficient is significantly different from zero.

d) Which of the two correlation coefficients do you think is a more appropriate summary of the relationship between the variables and why?

Question 6 -

A study discussed the relationship between cigarette smoking and the mortality index for mouth cancer in men. The subjects were residents of 16 regions of Great Britain, Norway, and Sweden. The objective of the study was to determine whether a linear relationship between the variables was appropriate. The data are given in the file data2_Q6.sav.

a) Construct a scatter plot of mouth cancer mortality index against cigarette smoking amount. (3 marks)

b) Fit a regression line with the smoking amount as the independent variable (x) and mortality index as the dependent variable (y). Can you write down the linear relation between y and x? (hint: y = a+bx, what is the value a and b?)

d) Add the regression line to your plot and interpret your results.

Question 7 -

Use appropriate T-Test :

It is known, as a result of testing over many years, that the mean functional lifespan of an established dental operating lamp under normal working condition is 360 hours. A new lamp has recently come to the market, costing 5% more, and a dental practitioner has tested 25 of them. He finds that the mean functional lifespan of these lamps is 380 hours, with an estimated standard deviation of 30 hours. Is it worth his while investing in the new lamps or should he stick with the old?

Question 8 -

Can quitting smoking improve oral health condition (which can be measured using Oral Health index) over 12 months? A team of researchers is planning a study to examine this question. Based on the results of a previous study, they are willing to assume a standard deviation of 5 for the percentage change in Oral Health index over the 12 month period. An increase in Oral Health index of 2 percent (effect size) would be considered clinically important. Assuming the data can be considered normally distributed, the researchers will conduct a two-sided test with a Type I error of 5% and are willing to accept a power of 0.80.

Using the on-line calculator in the link below:

https://www.stat.ubc.ca/~rollin/stats/ssize/

a) Perform a calculation to determine whether a sample of 30 subjects is a large enough sample to give the required power. 

b) Estimate the smallest sample required to give a power of at least 0.9.

c) If Type I error is controlled as 0.01, and power needs to reach 0.9, what is the smallest sample size needed?

d) If I consider 4 percent of change in Oral Health index as clinical importance, given the required type I error as 5% and power as 0.8, what is the sample size needed?

e) How would you interpret the relation between sample size, significance level, power and effect size?

Attachment:- SPSS Questions.zip