1. “Victor Babes” UNIVERSITY OF MEDICINE AND PHARMACY TIMISOARA
DEPARTMENT OF
MEDICAL INFORMATICS AND BIOPHYSICS
Medical Informatics Division
2007 / 2008 1 1 1 1

2. STATISTICAL ESTIMATION STATISTICAL TESTS (I)
COURSE 4 2 2 2 2

3. STATISTICAL ESTIMATION2 2 2 2

4. 1.1. Numerical variables - example
A STUDY ON CHILDREN SOMATIC DEVELOPMENT
N = 25 children, age 10, Timisoara, 1997
mean X = 137 cm
standard deviation s = 5 cm
Can we extend conclusions to the entire population?
For several samples, various averages!

5. 1.2. GRAPHICAL REPRESENTATIONS Individual values – continuous line Sample means – dotted line

6. 1.3. Population characteristics
Population mean μ
Standard error of the mean

7. EXAMPLE A STUDY ON CHILDREN SOMATIC DEVELOPMENT
N = 25 children, age 10, Timisoara, 1997
mean X = 137 cm
standard deviation s = 5 cm
standard error of the mean sx = 1 cm

8. 1.4. LOCALIZATION OF POPULATION MEAN

9. 1.5. DEFINITIONS a) STANDARD DEVIATION=
DISPERSION INDICATOR SHOWING INDIVIDUAL VALUES SPREADING AROUND SAMPLE MEAN
b) STANDARD ERROR OF THE MEAN=
DISPERSION INDICATOR SHOWING SAMPLE MEAN SPREADING AROUND POPULATION MEAN

10. EXERCISE
For a group of N = 36 cardiac patients we found the mean blood systolic pressure of 150 mm Hg with a standard deviation of 12mm.
a) In which interval are there located 68% of patient systolic pressure values ?
b) In which interval can we find the mean systolic pressure with 95% probability ?
c) What percent of pacients have values above 162 ? 8 8 8 8

11. 1.6. Generalization LOCATION OF POPULATION CAHARACTERISTICS TYPES:
MEANS
PROPORTIONS
DIFFERENCES (MEANS, PROPORTIONS) 3 3 3 3

12. 1.6.a. MEAN ESTIMATION LARGE SAMPLES N > 30 X = NORMAL DISTRIBUTION
(REGARDLESS INDIVIDUAL DISTRIBUTION)
68% %
90% %
95% %

13. 1.6.b. SMALL SAMPLES N < 30 1.6.c. PROPORTIONS X - t DISTRIBUTION
DEGREES OF FREEDOM
1.6.c. PROPORTIONS 10 10

14. STATISTICAL TESTS 2 2 2 2

15. 2. STATISTICAL TESTS 2.1. SIGNIFICANT AND NONSIGNIFICANT DIFFERENCES
a) Example:
BOYS GIRLS
n = 25 n = 25
X = 137 cm X = X = 139.5
s = 5 cm s = 5
sx = 1 cm sx = 1
(135, 139) ...95% nonsignificant significant 12 12

16. b) DEFINITIONS NON-SIGNIFICANT DIFFERENCES
High probability to occur by chance
Sampling variability
The two samples belong to the same population
SIGNIFICANT DIFFERENCES
Low probability to occur by chance
Must have another cause 11 11

19. 2.2. STATISTICAL HYPOTHESES
a) NULL HYPOTHESIS
H0 : X1 = X2 ( not mathematical equal, but statistical!)
There are no significant differences between the two values (samples)
b) ALTERNATE HYPOTHESES
H1 : X1  X2 (bilateral)
X1 > X2 , X1 < X2 (unilateral) 9 9 9 9

20. 2.3. SIGNIFICANCE THRESHOLD
a) DEFINITION:
value of probability below which we start consider significant differences
b) VALUE:
a = 0.05 = 5 %
c) CONFIDENCE LEVEL
1 - a = 0.95 = 95 %
2.4. P COEFFICIENT
P = probability that the observed differences have occurred by chance (sampling variab.) 13 13

21. 2.5. DECISION
If p > 0.05 => Non-significant differences, (N) , H0 accepted
If p < 0.05 => Significant differences, (S), H0 rejected
If p < 0.01 => Very significant differences, (V), H0 rejected
If p < => Extremely significant differences, (E) 24 24

22. 3. TESTS CHARACTERISTICS
3.1. ERRORS
TYPE I: H0 = TRUE, BUT REJECTEED
TYPE II: H0 = FALSE, BUT ACCEPTED
3.2. TEST CONFIDENCE = 1 - a
TEST POWER = 1 - b
inverse proportionality 3 3 3 3

23. 3.3. Parametric and nonparam.
Parametric - for normal distributed variables
Nonparametric - for other distributions
4. CLASSES OF TESTS
SIGNIFICANCE TESTS
HOMOGENEITY T.
CONCORDANCE T.
INDEPENDANCE T.
CORRELATION COEFICIENT TESTS 8 8 8 8

24. - e n d - 30 30