Mereesha.k

8/13/2019 Mereesha.k

1/30


2/30

Tests of significance

Parametric tests

Eg. T test, Z test, Chi-square test,

Pearson correlation coifficient

Non parametric tests

Eg. Chi-square test, Kruskal-Wallis test, Spearman

correlation coifficient


3/30

Tests of significance- Steps involved

Define the problem

state the hypothesis

Null hypothesis

Alternate hypothesis

Fix the level of significance

Select appropriate test to find test statisticFind degree of freedom (df)

Compare the observed test statistic with theoretical one at

desired level of significance & corresponding DF

If the observed test statistic value is greater than the theoreticalvalue, reject the null hypothesis.

Draw the inference based on the level of significance


4/30

First variable Second

variable

Example Tests of significance

Quantitative Quantitative Water F levels andmean DMFT Pearson correlationcoefficient (r) ;

linear regression

Quantitative Ordinal Water F levels and

esthetic concerns

Spearman correlation

coifficient (rho); possibly

use ANOVA or F test

Quantitative Dichotomous

unpaired

Tooth

displacement in

mm in males and

females

Students t- test

Or

Z- test

Quantitative Dichotomous

paired

Difference in systolic

blood pressure before

and after injecting LA

Paired t- test

Or

Z- test

Quantitative nominal Mean DMFT in

four areas

ANOVA (F- test)

Tab.1. Appropriate tests of significance to be used in bivariate analysis


5/30

Tab.3. Appropriate tests of significance to be used in bivariate analysis

First variable Second variable Example Tests of significance

Dichotomous Dichotomous

unpaired

Success/ Failure in

treated/untreated groups

Chi- square test; Fisher exact

probability test

Dichotomous Dichotomous

paired

Change in success/ failure

before and after treatment

Mc Nemar chi- square test

Dichotomous nominal Retention of different pit and

fissure sealants two years after

application

Chi- square test

nominal nominal Sterilising equipment used by

doctors of different

specialities

Chi- square test


6/30

Tab.4. Appropriate tests of significance to be used in multivariate analysis

dependent variable independent

variables

Example Tests of significance

Quantitative All are categorical Prevalence of dental caries

- frequency of sugar intake,

water fluoride level, socio

economic status

ANOVA

Quantitative All are quantitative Blood pressure- body mass

index, age, amount of fat

intake, salt intake

Multiple linear

regression


7/30

Objective of using tests of significance

To comparesample mean with population

Means of two samples

Sample proportion with population

Proportion of two samplesAssociation b/w two attributes


8/30

t - test

Students t-test

Designed by W.S GossettUnpaired t- test (two independent samples)

Paired t- test ( single sample correlated observation)

Essential conditions:

randomly selected samples from the corresponding

populations

Homogeneity of variances in the 2 samples

Quantitative data

Variable normally distributed

samples < 30


9/30

Unpaired t- test

Unpaired data of independent observation made on the

individual of two different or separate groups or samplesdrawn from 2 populations

Null hypothesis is stated

difference between means of two samples

(X1-X2) measures variation in variable

calculate the t value

t = (X1-X2)

SE


10/30

SE =

Determine degrees of freedom

df= (n1-1 )+(n2- 1) = n1+ n2-2

Compare calculated value with table value at particular

degrees of freedom to find the level of significance

1n1+ 1n2 If t- not known


11/30

t value at 5% level2.0692.74obtained value in expSignificant


12/30

Paired t- test

To study the role of factor or cause when the observations aremade before & after the its play:

Eg: exertion on pulse rate, effect of a drug on blood pressure etc

To compare the effect of 2drugs , given to the same individualin the sample on two different occasions

eg: adrenaline & noradrenaline on pulse rate

to study the comparative accuracy of 2 difft instruments

eg: 2 difft types of sphygmomanometers

to compare the results of 2 difft lab techniques

To compare the observations made at two different sites in thesame body


13/30

Testing procedure:

Null hypothesis

X1-X2= x

Calculate mean of the difference x = x /ncalculate SD of differences & SE of mean

SE= SD/ n

Determine t value

t = x -o

SD / n= x

SD/ n

Find the degrees of freedom , n-1refer the table & find the probabilityP >0.05 not significantP< 0.05 significant


14/30


15/30

T value 5 % =

2.31

Observed tvalue 5.17

HS


16/30


17/30

Analysis of variance

ANOVA test

Compare more than two samples

Compares variation between the classes as well as withinthe classes

For such comparisons there is high chance of error using t

test.


18/30

A :b/w groups variation = random variation (always) +imposed variation (maybe)

B :Within group variation = random variation

Total variation = A+B

If there is no real difference b/w groups, then

between treatment = random variation = 1

Within treatment random variation


19/30

If there is any real difference b/n the R/

between treatment = random variation+ imposed variation

Within treatment random variation > 1


20/30

Chi square test ( test )

Non parametric testDeveloped by Karl Pearson

Not based on normal distribution of any variable

Used for qualitative data

To test whether the difference in distribution of

attributes in different groups is due to sampling

variation or otherwise.


21/30

Applications

1. Test for goodness of fit

2. Test of association (independence)

3. Test of homogeneity or population variance

2test is non parametric in the first two cases and

parametric in the third case


22/30

Calculation of valueThree requirements

A random sampleQualitative data

Lowest expected frequency > 5

= (observed fexpected f )

df =( r-1)x (c-1)

Calculated value is correlated with table

Expected fExpected f = row total x column total / grand total


23/30

To test whether there is any association between dental

hygiene no of cavities

df = 2 p value at 5 % is 5.99

Calculated value7Null hypothesis is rejected


24/30


25/30

Drawbacks :

Tells us about the association but fails to measure the strength of

association.

Test is unreliableifthe expected frequency in any one cell

is less than 5.

Correction is done by subtracting 0.5 from [ O-E ] Yatess correction

For Tables larger that 2 x 2 , Yates correction cannot be applied

Not applicable when there is 0 or 1 in any of the cells [ Resort toFishers exact probabilitytest ]

values interpreted with caution when sample < 50


26/30

Non parametric tests

a family of statistical tests also called as distribution free

tests that do not require any assumption about thedistribution the data set follows and that do not require the

testing of distribution parameters such as means or variances


27/30

Friedmans test nonparametric equivalent of analysis of

varianceKruskalWallis testto compare medians of severalindependent samples equivalent of oneway analysis ofvariance

MannWhitney U testcompare medians of two independentsamples. Equivalent of t test

McNemars test variant of chi squared test , used when data ispaired

Wilcoxons Sign rank test paired dataSpearmans rank correlation correlation coefficient


28/30

Conclusion

Its more important to understand the indications and limitations

of various statistical tests rather than the robust mathematical

calculations since the latter is taken care of by the software like

SPSS

Understanding the classification of data is crucial for the

selection of appropriate test of significance


29/30

References

B.K. Mahajan. Methods in Biostatistics, 6thedition.

P.S.S.Sundar Rao, J.Richard. An introduction to Biostatistics,3rdedition.

James F Jekel, David L Katz, Joann G Elmore. Epidemiology, biostatistics

and preventive medicine, 2ndedition.

Research methodology-C.R.Kothari,


30/30

Documents

Mereesha.k