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:OrderedRelative 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 : Chi square test

Fisher exact test 2. Ordinal : 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 valueNominal data: Chi square test bestContingency table No. of rows and columns eg, 2x4

2x2 Contingency table

A B

+

_

Chi Square test:x²= sum of (observed – expected no. of

individuals in a cell)² / expected no. of individuals in a cell.

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

orSensitivity of a test is the probability that

it will correctly diagnose a caseScreening 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)

SummaryStatistical 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.