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Biostatistics II

Dr Fayssal M Farahat MBBCh, MSc, PhD Consultant Public Health

Infection Prevention and Control Department

Assist Professor, Public Health

King Saud bin AbdulAziz University for Health Sciences

King AbdulAziz Medical City, Jeddah, SA

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Random Error

Wrong result due to chance

20%

Sample Size

precision

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Measurement

Observer

Round down BP

Leading Q

Instrument

Subject Recall bias

(breast cancer and dietary fat)

Calibration

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Systematic Error

Wrong result due to BIAS

Sample (respondents) or

Measurement (unclear Q)

OR

Accuracy

Sample size

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Accuracy and Precision

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Content

validity

Face validity

Subjective judgment

Sampling validity QOL: social, physical, emotional

Construct

validity

Criterion- related

validity

Depressed and healthy

Measure of depression

if could predict suicide (future outcome)

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Confounding Variable

Exposure Disease

Confounding

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Types of hypotheses

NULL Ho NO association between predictor and outcome

No difference between the aspirin and placebo

The formal basis for testing statistical significance

The association observed in a study is due to chance

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ALTERNATIVE H1

association between predictor and outcome

Accepted by default,

if test of significance

rejects the null hypothesis

Types of hypotheses

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Truth in the population

Association between

predictor and outcome

No Association between

predictor and outcome Results in the

study sample

Reject

null hypothesis

Fail to Reject

null hypothesis

Correct Type I error

Type II error Correct

alpha

beta

False +ve

False -ve

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False +ve

The investigators can reject the null hypothesis and conclude that there is a difference between the two treatment groups, when in fact there is no such difference exist.

The probability of making such error is called

p value

ART

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False negative

The investigators may fail to

reject the null hypothesis that

there is no difference between

the two interventions, when in

fact there is difference.

The probability of making such error is called

Beta

BAF

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CI vs. P Value

Significance and precision

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Statistic and clinical significance

Statistically sig results might not be clinically

sig.

Statistically non sig results might be still

clinically sig.

Effect of Bupropion on smoking cessation=

OR= 2.35 , P > 0.05 nothing to tell regarding

clinical importance

OR= 2.35 (0.85, 6.47), CI lying in the side that

favor treatment > 1 = there is a trend of positive

effect of this medication

clinical sig although statistically non sig.

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Commonly used statistical tests

Chi-square test: To examine the relationship

(association or difference) between two

categorical variables.

2 by 2 or r by c

Lung

cancer

control

smokers A B

Non-smokers C D

McNemar’s test

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Cont. statistical tests

Paired t test: used to compare the means of

one variable in the same group (pre and post

an event).

Wilcoxon’s matched pairs test

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Cont. statistical tests

Student’ t test: To evaluate the difference in

means between two groups

Mann-Whitney test

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Cont. statistical tests

ANOVA (F test): To test for the difference of means of the same variable between more than two groups.

Kruskall-Wallis test

LSD: To test for the difference of the means of the same variable between each two groups individually.

Following a significant F test

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19 Time

Positive

No relation

Negative

Vari

ab

le

X

Y

+

-

0

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Non parametric statistics

If sample size is very small “as small as 10”

Abnormally distributed data

– Via histogram

– Performing a normality test.

Scale of measurements (scores, titer).

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Statistically non significant findings are of the

same importance as statistically significant

findings.

Be sure of the distribution of your data before

doing any statistical analysis.

Student’s t test, Mann Whitney,

Sign and Wilcoxon Signed

Rank Tests

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• A single group of subjects and the goal is to compare an observed value or a norm or standard.

• A single group that is measured twice and the goal is to estimate how much the mean in the group changes between measurements.

• To determine if a difference exists between 2 independent groups.

Group 1

Mean 1

SD 1

N 1

Group 2

Mean 2

SD 2

N 2

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Assumptions for the t distribution

Assumption # 1

• The observations in each group follow a

normal distribution.

• Violating assumption of normality gives p

values that are lower than they should be,

making it easier to reject the null

hypothesis and say there is difference

when none exist.

Assumption # 2

• SDs in the two samples are equal

(homogenous variances).

• The null hypothesis states that the two

means are equal, or from the same

population, so SDs are equal.

• This assumption can be ignored when the

sample sizes are equal.

• t test is robust with equal sample sizes.

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Assumption # 3

• Independence= knowing observations in one group tells us nothing about the observations in the other group.

• In the paired t test, we can expect that a subject with relatively low value at the first measurement to have a relatively low second measurement as well.

• No statistical test can tell us about independence, so the best way is to design properly to ensure they are independent.

Wilcoxon Signed Rank Test

• No disadvantage in using Wilcoxon signed

rank test in any situation with a small

sample size, even when observations are

normally distributed.

• Non parametric statistic when paired t test

is not the appropriate.

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Mann-Whitney-Wilcoxon rank test

• Whether medians are different.

• Rank all observations, then analyze the

ranks as they were the original

observations.

• Mean and standard deviation of the ranks

are calculated for the t test.

• Test the hypothesis that the means of the

ranks are equal in the two groups.

Association between exposure of women to pesticides

during pregnancy and birth defects in their offspring

using data from a cohort study.

Exposure Birth defects

Yes

Birth defects

No

Total

Yes 20 980 1000

No 25 3975 4000

Total 45 4955 5000

Incidence (of birth defects) in exposed 20/1000= 0.02

Incidence (of birth defects) in unexposed 25/4000= 0.00625

Relative Risk 0.02/0.00625= 3.20 (1.78, 5.74)

If you would like to calculate Odds Ratio?

(20 X 3975) / (25 X 980) = 3.24 (1.79, 5.87)

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The most important is to

understand the concepts to

interpret the clinical

research.