Statistical test for Non continuous variables. Dr L.M.M. Nunn.
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Transcript of Statistical test for Non continuous variables. Dr L.M.M. Nunn.
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.