Transcript Statistical_test_non_continuous_variables

Statistical test for Non
continuous variables.
Dr L.M.M. Nunn
What does the term
“statistics” mean?
 A statistic is an estimate, based on random
sampling of the population, of parameters of
the population.
 Emphasis on statistical analysis in research
 P < 0.05 Statistically significant
 P > 0.05 Statistically insignificant
 Statistical testing > individual data points

Probability:
 Numerical likelihood of the occurrence of an
event.
 Significant: p < 0.05
 Why 5% as level of statistical significance?
 If p < 0.05, it means that the likelihood that
the event was due to chance is < 5%.
 Thus > 95% certainty that the event was not
due to chance.
Hypothesis testing:
 Likely or unlikely to occur.
 Convert question into Null hypothesis
 H0 = No difference between sample +
population.
H1 = Alternate hypothesis
= what you are trying to prove
Hypothesis testing (cont.)
 Example : Aspirin vs placebo in MI patients
 H0: aspirin = placebo
 H1: Aspirin > placebo
 If α < 0.05: reject null hypothesis and
accept H1.
 i.e. Aspirin more advantageous than
placebo in MI patients.
Variables:
Ordinal:
Ordered
Relative rather than absolute relations
btw variables:
 eg: Apgar scores
Power (1- 5)
Level of pain (0 – 10)
Nominal variables:
 Named
 Quality rather than quantity
 eg. Female + Male
Alive + dead
EEG waveforms (α, β, θ, δ)
Quantitative Variables:
A. Discrete:
Limited no of possible variables
eg. No. of previous pregnancies
No. of cases of acute cholecystitis
B. Continuous variables
Unlimited no of possible variables
eg. height, weight
Selecting appropriate
statistical test:
1. Nominal
2. Ordinal
:
Chi square test
Fisher exact test
: Parametric (Normal
distribution, large sample
size)
Non parametric test
(Abnormal distribution
small sample size) .
3.Continuous variables: Analysis of
linear regression.
Contingency tables:
 Ordinal & nominal scales different
techniques available for presentation +
analysis of results
Histograms are of limited value
Nominal data: Chi square test best
Contingency table
 No. of rows and columns eg, 2x4
2x2 Contingency table
A
+
_
B
Chi Square test:
sum of (observed – expected no. of
individuals in a cell)² / expected no. of
individuals in a cell.
 x²=
 x²
= Sum of (0 – E)²
E
Observed frequencies similar to
expected frequencies then x² = small
no. i.e. statistical insignificant.
Observed + expected frequencies differ
then X² = big no. and statistically
insignificant
Chi Test (continued):
Test whether data has any given distribution
Frequency table yielding observed
frequencies.
Probabilities calculated for each category
Probabilities converted into frequencies =
expected frequencies
Compare observed frequencies with
expected frequencies.
Observed frequencies similar to
expected frequencies, then the
observed frequency distribution is well
approximated by hypothesis one.
Fisher Exact Test:
The Chi square test used to analyze
2x2 contingency tables when frequency
of observations in all cells are at least 5
In small studies when expected
frequency is <5: Fisher Exact test
Turns liability of small sample sizes into
a benefit.
Sensitivity:
Proportion of cases correctly diagnosed
by a test = sensitivity
or
Sensitivity of a test is the probability that
it will correctly diagnose a case
Screening test eg. Rapid HIV
Specificity:
Proportion of non cases correctly classified by
a test.
Or
Specificity represents the probability that a
non case will be correctly classified
If a +ve test results lead to major intervention
eg, colectomy, mastectomy, a high specificity
is essential.
Test lacks specificity a substantial no. of
people may receive unnecessary & injurious
treatment.
Predictive value:
Predictive value of a test depends on
the prevalence of disease in the
population of patients to whom it is
applied.
Disease
Test
+
-
+
TP
FP
-
FN
TN
Sensitivity =
TP
(TP + FN)
Specificity =
TN
(TN + FP)
Positive predictive value =
TP
(TP + FP)
Negative predictive value = TN
(FN + TN)
Summary
 Statistical
tests provide the investigator
with a “p” value.
 Choose the correct Statistical test
according to the appropriate Variable.
 “p” value < 0.05, Statistically
significant,Null hypothesis is rejected
and Alternate hypothesis accepted.