ebd1 lecture7 2010

General Studies 1D

Evidence-Based Dentistry 1

Lecture 7

Statistical Tests

© The University of Adelaide, School of Dentistry

Biostatistics

Descriptive statistics

Inferentialstatistics

Recap…


Descriptive statistics

Central tendency

Mean, median, mode

Describing summary data

Central dispersion

Variance, sd, range, iqr


Inferential statistics

Estimation

Point estimate

Mean

Confidence interval

95% CI

Inferring study result to reference population

Hypothesis testing

Ho & HA

p-value


Types of statistical tests

t-test

ANOVA

Chi-square test

Regression

Correlation


The t-test

Appropriate whenever you want to compare the means of two groups.

Assesses whether there is a statistically significant difference between two group means.

Eg. You want to compare the weights in 2 groups of children, each child being randomly allocated to receive either a dietary supplement or placebo


Types of t-test

• One sample compare with population

• Unpairedcompare with control

• Pairedsame subjects: pre and post


Types of t-tests 1) One sample t-test:H0: = 0

test if a sample mean for a variable differs significantly from the given population with a known mean

2) Unpaired- or independent samples- t-test: H0: 1 = 2

test if the population means estimated by 2 independent samples differ significantly (e.g. group of male and group of females)

3) Paired- or dependent- samples t-testtest if the population means estimated by dependent samples differ significantly (e.g. mean of pre and post treatment for same set of patients)


One sample t-test: Test if a sample mean for a variable differs significantly from the given population with a known mean exampleDo middle-aged Caucasian male dentists have higher or lower blood pressure than the general population?

Blood pressure for Caucasian males aged 35-44 yrs: 0=127.

Sample of 72 Caucasian male dentists aged 35-44 years: xbar=127 and s=7.

Hypotheses: H0: =127mm Hg vs. HA: 127mm Hg. Find that P-value for this one-sample t-test is 0.279. Since P-value > 0.05, we retain H0, i.e. the sample was

drawn from a population where =127. We say that there is not a significant difference between

the sample mean and the population mean at the 5% leveli.e. the blood pressure of male dentists does not differ significantly from other men.


Independent-samples (or unpaired) t-test: Test if the population means estimated by 2 independent samples differ significantly (e.g. group of male and group of females)exampleIs the average height between males and females enrolled

in EBD1 significantly different?

Descriptive statistics:Females: xbar=164.7, s=5.92, n=58 Males:xbar=177.6, s=7.27, n=31QuestionDo these data support the contention that male and female EBD1 students differ in average height?. The hypotheses are H0: 1=2 and HA: 12

Results: An independent samples t-test in SPSS produces a P-value<0.0001 indicating that there is evidence that males and females differ significantly in mean height (males being taller). The small P-value indicates that there is a very small probability that this difference occurred by chance.


Independent t test ……

What hypotheses ? Comparing 2 population

means Ho:


Independent t test (example)……

What hypotheses ? Association between age and periodontal

disease? Comparing mean age between those with

periodontal disease and those without periodontal disease

Ho:


6337N =

Presence of periodontal disease

NoYes

95%

CI o

f mea

n ag

e (y

ears

)

43

42

41

40

39

38

37

"The means age of 2 groups are not significantly different (P=.232). Therefore there is no significant association between age and Periodontal."

(-3.9, 1.0)


Dependent-samples (or paired) t-test: example

Suppose I gave you all the EBD1 test before lectures and tutorials commenced. After attending the 6-week EBD1 unit, suppose I gave you the EBD1 test again.

I end up having, for each of the 119 students in the class, 119 pre-test and 119 post-test scores. I subtract the pre-test score from the post-test score to obtain an improvement (hopefully!!) for each student. These 119 differences form a single sample.

To assess whether attending the EBD1 course significantly improved students comprehension of EBD, we test H0: =0 vs. HA: >0

H0 says that no improvement occurs, while HA says that post-test scores are higher on average. We calculate the mean difference in the sample and the standard deviation.

Hopefully, a P-value<0.05 is obtained so we can reject H0 of no difference and conclude that the improvement in test scores was unlikely to have occurred by chance alone and therefore there is strong evidence that the EBD1 course was effective in raising the scores!


Paired t test (example)……What hypotheses ? Any change in Knowledge-score after

intervention? To test the mean of score difference (Post –

Pre) is different from zero or not? Ho:


The mean of score difference (between pre- and post-intervention scores) is significantly different from zero (P<.001).

We observe that post-I score is higher than pre-I score.

100100N =

Post-Int. ScorePre-Int. Score

95%

CI o

f mea

n sco

re

16

15

14

13

12

11

10

9

8


ANOVA An ANOVA (Analysis of Variance),

sometimes called an F test, is a test that measures the difference between the means of two or more groups

It is closely related to the t test - the major difference is that, where the t-test measures the difference between the means of two groups, an ANOVA tests the difference between the means of two or more groups.

For i groups, the null hypothesis is: H0: 1 = 2 = 3 …. = i ..(all group means in the population are equal

HA: At Least 1 group mean in the population differs from the others


ANOVA (example)……What hypotheses ? Association between educat.level and knowledge score? Comparing mean knowledge score (kscore) among 3

education levels Ho:


a One-way ANOVA test

a

b


343234N =

Level of education

secondary and higerprimary schoolno schooling95

% C

I of m

ean k

nowl

edge

scor

e

18

16

14

12

10

8

6

4

1. The ANOVA test is significant (P<.001).

2. Therefore, there is significant association between level of education and knowledge score.

3. We observe that those with higher the education level had higher knowledge scores.


Chi-square test

Used to test the strength of the association between qualitative variables (or categorical data).

Hypothesis:H0: No association between variables

Ha: The two factors are associated in the population


What hypotheses ? Comparing 2 or more proportions Ho: P1=P2=P3

Chi-square test ……


Hypothesis….

Association between gender and Perio. disease

Comparing the proportion of Perio disease between male and female

Ho: P(perio)male = P(perio)female

Example…


The prevalence (proportion) of PO between male and female are not significantly different (P = 0.753). Therefore, there is no significant association between gender and PO.

a

b

c

ebd1 lecture7 2010

Technology

sample ttest

dependent samples ttest

unpaired ttest

independent samples

ttest appropriate

independent samples

types of t

given population