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Faculty of Medicine Department of Cancer Research and Molecular Medicine

Exam ST3001

Introduction to Medical Statistics

Friday May 25th, 2012, 09.00 a.m. 1:00 p.m

ECTS credits: 7.5 Allowed examination support (code A): Calculator, all written and printet aids.

No. pages (including front page): 7

Contact person during the exam: Grethe Albrektsen, mob. 954 98 743

Exam results: June 18th 2012 Examination results are announced on http://studweb.ntnu.no/

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IMPORTANT - Read the exercises carefully (all parts) before answering. - Your answers should be short and precise. - Remember to mark your answers with ordered numbers

corresponding to exercise. You do not need to repeat the text to exercises in your answers.

EXERCISE 1. Mean value and standard deviation are common measures of central location (typical value) and spread for a continuous, normally distributed variable. a) What can you say about distribution of values of a continuous, normally

distributed variable that has expected value (mean) 2.5 and standard deviation of 1?

b) What is the standard error a measure of? c) How is the median value defined, and when is the median value a suitable

measure of central location (typical value) in an empirical data set? d) What would give a suitable graphical display of distribution of values of a

continuous variable?

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EXERCISE 2 Height and weight are registered annually for young people who attend the Norwegian military service. The recruits can be considered to be a representative sample from the Norwegian population (specific to age and gender). In one study, they want to utilize these data to examine whether body mass index (BMI) have changed during a 10-year period (from 2000 to 2010).

a) What statistical test method (methods) can be applied to examine whether BMI

(on continuous scale) among 19-year old boys differ in 2000 and 2010? Give a short description of what is tested (compared), in view of the method you have chosen

assumptions on the statistical test method(s) you have chosen

b) BMI can be categorized into 4 different categories: underweight, normalweight, overweight, and extreme overweight. what statistical test method (methods) can be applied to examine whether BMI (categorized variable) differ in 2000 and 2010? what are the assumptions on the statistical test method(s) you have chosen.

c) The researchers also want to examine whether BMI (on continuous scale) has

increased steadily each year from 2000 to 2010 (year considered as continuous variable). what statistical method (methods) can be applied to examine this question? give a short description on assumption(s) on the statistical method(s) you have chosen.

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EXERCISE 3 In a study comprising 60 persons that did not exercise regularly, blood serum cholesterol-level was measured before and after a 4-weeks intervention-period consisting of organized training (moderate to high intensity). Cholesterol levels before and after intervention is registered on the data file with variable names CHOLbefore and CHOLafter, respectively. The main aim of the study was to examine whether the intervention (physical exercise) influenced on cholesterol level. Analysis of data by means of a paired (one-sample) T-test gave the following results (SPSS output):

Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 CHOLbefore 5.566 60 .4937 .0637

CHOLafter 5.390 60 .6581 .0850

Paired Samples Correlations

N Correlation Sig.

Pair 1 CHOLbefore & CHOLafter 60 .766 .000

Paired Samples Test

Paired Differences

Mean Std. Deviation

Std. Error

Mean

95% Confidence Interval of the

Difference

Lower Upper

Pair 1 CHOLbefore - CHOLafter .1763 .4232 .0546 .0669 .2856

Paired Samples Test

T Df Sig. (2-tailed)

Pair 1 3.226 59 .002

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a) Why is a paired (one-sample) T-test applied?

b) Define the null hypothesis and the alternative hypothesis for the statistical test (paired T-test, two-sided test), in terms of value of parameter tested interpretation (give a short description)

c) What do the p-value for the statistical test (paired T-test) express? in terms of probability-distribution of test statistic general interpretation

d) What is the assumption(s) on this statistical test (paired T-test)

- what alternative statistical method (test) could have been used if the assumption(s) is not met?

e) Describe results from the analysis, based on information from the SPSS output. Report estimated value (point- and interval estimate) of change in cholesterol-level result from the statistical test

f) It is possible to make an error, i.e. draw the wrong conclusion, when results from our study (based on analyses of empirical data, sample) are transferred to population level (generalization of results). - what type(s) of error is possible to do?

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EXERCISE 4 In a study among children and adolescent aged 3-19 years, a simple linear regression analysis was applied to examine association between age (1-year intervals) and lung capacity, measured by forced expiratory volume, FEV (litre/sec.). Analysis of data gave the following results (SPSS output):

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate

1 .756a .572 .572 .56753

a. Predictors: (Constant), age

ANOVAb

Model

Sum of

Squares df Mean Square F Sig.

1 Regression 280.919 1 280.919 872.184 .000a

Residual 210.001 652 .322

Total 490.920 653

a. Predictors: (Constant), age

b. Dependent Variable: fev

Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

95.0% Confidence

Interval for B

B Std. Error Beta

Lower

Bound

Upper

Bound

1 (Constant) .432 .078 5.541 .000 .279 .585

Age .222 .008 .756 29.533 .000 .207 .237

a. Dependent Variable: fev

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a) Define the linear regression model (mathematical expression) that describes the linear relationship between age (in years) and lung capacity, measured by FEV. Utilize information in the SPSS output.

b) How do you interpret the value of the regression coefficient? c) What is expected value of FEV for a 10-year old child, based on the linear

regression model? d) Is it a strong linear relationship between age and lung capacity, measured by

FEV? Argue for your answer.