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 : 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 value  Nominal data: Chi square test best  Contingency 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 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.