SlideShare a Scribd company logo
1 of 23
CHI SQUARE TEST
CONTENTS:
•IMPORTANT TERMS

•INTRODUCTION

•CHARACTERISTICS OF THE TEST

•CHI SQUARE DISTRIBUTION

•APPLICATIONS OF CHI SQUARE TEST

•CALCULATION OF THE CHI SQUARE

•CONDITION FOR THE APPLICATION OF THE TEST

•EXAMPLE

•YATE’S CORRECTION FOR CONTINUITY

•LIMITATIONS OF THE TEST.
IMPORTANT TERMS
1) PARAMETRIC TEST: The test in which, the population
   constants like mean,std deviation, std error, correlation
   coefficient, proportion etc. and data tend to follow one
   assumed or established distribution such as normal,
   binomial, poisson etc.

2) NON PARAMETRIC TEST: the test in which no constant of a
   population is used. Data do not follow any specific
   distribution and no assumption are made in these tests. E.g.
   to classify good, better and best we just allocate arbitrary
   numbers or marks to each category.

3) HYPOTHESIS: It is a definite statement about the population
   parameters.
4) NULL HYPOTHESIS: (H0) states that no association exists
   between the two cross-tabulated variables in the population,
   and therefore the variables are statistically independent. E.g.
   if we want to compare 2 methods method A and method B for
   its superiority, and if the assumption is that both methods are
   equally good, then this assumption is called as NULL
   HYPOTHESIS.

5) ALTERNATIVE HYPOTHESIS: (H1) proposes that the two
   variables are related in the population. If we assume that
   from 2 methods, method A is superior than method B, then
   this assumption is called as ALTERNATIVE HYPOTHESIS.
6) DEGREE OF FREEDOM: It denotes the extent of
   independence (freedom) enjoyed by a given set of observed
   frequencies Suppose we are given a set of n observed
   frequencies which are subjected to k independent
   constraints(restrictions) then,

  d.f. = (number of frequencies) – (number of independent
                                      constraints on them)
  In other terms,
                        df = (r – 1)(c – 1)
  where
               r = the number of rows
               c = the number of columns

7) CONTINGENCY TABLE: When the table is prepared by
   enumeration of qualitative data by entering the actual
   frequencies, and if that table represents occurance of two
   sets of events, that table is called the contingency table.
   (Latin, con- together, tangere- to touch). It is also called as
   an association table.
INTRODUCTION
The chi-square test is an important test amongst the several
 tests of significance developed by statisticians.

Is was developed by Karl Pearson in1900.

CHI SQUARE TEST is a non parametric test not based on any
 assumption or distribution of any variable.

This statistical test follows a specific distribution known as chi
 square distribution.

In general The test we use to measure the differences between
 what is observed and what is expected according to an
 assumed hypothesis is called the chi-square test.
IMPORTANT CHARACTERISTICS OF A CHI
           SQUARE TEST

 This test (as a non-parametric test) is based on
  frequencies and not on the parameters like mean and
  standard deviation.

 The test is used for testing the hypothesis and is not
  useful for estimation.

 This test can also be applied to a complex contingency
   table with several classes and as such is a very useful
  test in research work.

 This test is an important non-parametric test as no rigid
   assumptions are necessary in regard to the type of
   population, no need of parameter values and relatively
  less mathematical details are involved.
CHI SQUARE DISTRIBUTION:
If X1, X2,….Xn are independent normal variates and each is
distributed normally with mean zero and standard deviation
unity, then X12+X22+……+Xn2= ∑ Xi2 is distributed as chi square (c2
)with n degrees of freedom (d.f.) where n is large. The chi square
curve for d.f. N=1,5 and 9 is as follows.
If degree of freedom > 2 : Distribution is bell shaped

If degree of freedom = 2 : Distribution is L shaped with
                           maximum ordinate at zero

If degree of freedom <2 (>0) : Distribution L shaped with
                               infinite ordinate at the origin.
APPLICATIONS OF A CHI SQUARE TEST.
This test can be used in

1) Goodness of fit of distributions

2) test of independence of attributes

3) test of homogenity.
1) TEST OF GOODNESS OF FIT OF DISTRIBUTIONS:

 This test enables us to see how well does the assumed
  theoretical distribution (such as Binomial distribution,
  Poisson distribution or Normal distribution) fit to the
  observed data.

The c2 test formula for goodness of fit is:

                                    (o  e)
                                               2

                              
                        2

                                        e
 Where,
 o = observed frequency
 e = expected frequency

If c2 (calculated) > c2 (tabulated), with (n-1) d.f, then null
 hypothesis is rejected otherwise accepted.

And if null hypothesis is accepted, then it can be concluded
that the given distribution follows theoretical distribution.
2) TEST OF INDEPENDENCE OF ATTRIBUTES

Test enables us to explain whether or not two attributes are
 associated.

For instance, we may be interested in knowing whether a new
 medicine is effective in controlling fever or not, c2 test is
 useful.

In such a situation, we proceed with the null hypothesis that
 the two attributes (viz., new medicine and control of fever) are
 independent which means that new medicine is not effective
 in controlling fever.

c2 (calculated) > c2 (tabulated) at a certain level of
 significancfe for given degrees of freedom, the null hypothesis
 is rejected, i.e. two variables are dependent.(i.e., the new
 medicine is effective in controlling the fever) and if, c2
 (calculated) <c2 (tabulated) ,the null hypothesis is accepted,
 i.e. 2 variables are independent.(i.e., the new medicine is not
 effective in controlling the fever).

when null hypothesis is rejected, it can be concluded that there is
a significant association between two attributes.
3) TEST OF HOMOGENITY

 This test can also be used to test whether the occurance of
  events follow uniformity or not e.g. the admission of
  patients in government hospital in all days of week is
  uniform or not can be tested with the help of chi square
  test.

c2 (calculated) < c2 (tabulated), then null hypothesis is
 accepted, and it can be concluded that there is a uniformity
 in the occurance of the events. (uniformity in the admission
 of patients through out the week)
CALCULATION OF CHI SQUARE

                       (o  e)
                                 2

                
            2

                            e
Where,
O = observed frequency
E = expected frequency
If two distributions (observed and theoretical) are exactly alike,
c2 = 0; (but generally due to sampling errors, c2 is not equal to
zero)
STEPS INVOLVED IN CALCULATING c2

1) Calculate the expected frequencies and the observed
   frequencies:

   Expected frequencies fe : the cell frequencies that would be
  expected in a contingency table if the two variables were
  statistically independent.

  Observed frequencies fo: the cell frequencies actually
  observed in a contingency table.

          fe = (column total)(row total)
                                N
 To obtain the expected frequencies for any cell in any cross-
 tabulation in which the two variables are assumed
 independent, multiply the row and column totals for that cell
 and divide the product by the total number of cases in the
 table.
2) Then c2 is calculated as follows:



                           ( fe  fo )
                                            2

     c           
          2

                                       fe
CONDITIONS FOR THE APPLICATION OF c2
                TEST

The following conditions should be satisfied before X2 test can
be applied:

1) The data must be in the form of frequencies
2) The frequency data must have a precise numerical value and
   must be organised into categories or groups.
3) Observations recorded and used are collected on a random
   basis.
4) All the itmes in the sample must be independent.
5) No group should contain very few items, say less than 10. In
   case where the frequencies are less than 10, regrouping is
   done by combining the frequencies of adjoining groups so
   that the new frequencies become greater than 10. (Some
   statisticians take this number as 5, but 10 is regarded as
   better by most of the statisticians.)
6) The overall number of items must also be reasonably large.
   It should normally be at least 50.
EXAMPLE
YATE’S CORRECTION
If in the 2*2 contingency table, the expected frequencies are small
say less than 5, then c2 test can’t be used. In that case, the direct
formula of the chi square test is modified and given by Yate’s
correction for continuity




                        R1R2C1C2
LIMITATIONS OF A CHI SQUARE TEST

1) The data is from a random sample.

2) This test applied in a four fould table, will not give a reliable
   result with one degree of freedom if the expected value in any
   cell is less than 5.
   in such case, Yate’s correction is necessry. i.e. reduction of
   the mode of (o – e) by half.

3) Even if Yate’s correction, the test may be misleading if any
   expected frequency is much below 5. in that case another
   appropriate test should be applied.

4) In contingency tables larger than 2*2, Yate’s correction
   cannot be applied.

5) Interprit this test with caution if sample total or total of
   values in all the cells is less than 50.
6) This test tells the presence or absence of an association
   between the events but doesn’t measure the strength of
   association.

7) This test doesn’t indicate the cause and effect, it only tells
   the probability of occurance of association by chance.

8) the test is to be applied only when the individual
   observations of sample are independent which means that
   the occurrence of one individual observation
   (event) has no effect upon the occurrence of any other
   observation (event) in the sample under consideration.
THANK YOU

More Related Content

What's hot

What's hot (20)

Type i and type ii errors
Type i and type ii errorsType i and type ii errors
Type i and type ii errors
 
T test
T testT test
T test
 
Anova ppt
Anova pptAnova ppt
Anova ppt
 
Correlation and Regression
Correlation and RegressionCorrelation and Regression
Correlation and Regression
 
Chi – square test
Chi – square testChi – square test
Chi – square test
 
Parametric and non parametric test in biostatistics
Parametric and non parametric test in biostatistics Parametric and non parametric test in biostatistics
Parametric and non parametric test in biostatistics
 
01 parametric and non parametric statistics
01 parametric and non parametric statistics01 parametric and non parametric statistics
01 parametric and non parametric statistics
 
Null hypothesis AND ALTERNAT HYPOTHESIS
Null hypothesis AND ALTERNAT HYPOTHESISNull hypothesis AND ALTERNAT HYPOTHESIS
Null hypothesis AND ALTERNAT HYPOTHESIS
 
Measures of Central Tendency - Biostatstics
Measures of Central Tendency - BiostatsticsMeasures of Central Tendency - Biostatstics
Measures of Central Tendency - Biostatstics
 
Errors and types
Errors and typesErrors and types
Errors and types
 
Regression
RegressionRegression
Regression
 
Chi squared test
Chi squared testChi squared test
Chi squared test
 
Correlation analysis
Correlation analysisCorrelation analysis
Correlation analysis
 
F test
F testF test
F test
 
One way anova final ppt.
One way anova final ppt.One way anova final ppt.
One way anova final ppt.
 
Frequency distribution
Frequency distributionFrequency distribution
Frequency distribution
 
T test statistics
T test statisticsT test statistics
T test statistics
 
Measures of dispersion
Measures of dispersionMeasures of dispersion
Measures of dispersion
 
Non parametric tests
Non parametric testsNon parametric tests
Non parametric tests
 
Probability Distributions
Probability DistributionsProbability Distributions
Probability Distributions
 

Viewers also liked

Chi Square Worked Example
Chi Square Worked ExampleChi Square Worked Example
Chi Square Worked ExampleJohn Barlow
 
Null hypothesis for a chi-square goodness of fit test
Null hypothesis for a chi-square goodness of fit testNull hypothesis for a chi-square goodness of fit test
Null hypothesis for a chi-square goodness of fit testKen Plummer
 
Reporting chi square goodness of fit test of independence in apa
Reporting chi square goodness of fit test of independence in apaReporting chi square goodness of fit test of independence in apa
Reporting chi square goodness of fit test of independence in apaKen Plummer
 
Reporting Chi Square Test of Independence in APA
Reporting Chi Square Test of Independence in APAReporting Chi Square Test of Independence in APA
Reporting Chi Square Test of Independence in APAKen Plummer
 
Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Sneh Kumari
 
Functional matrix hypothesis revisited
Functional matrix hypothesis   revisitedFunctional matrix hypothesis   revisited
Functional matrix hypothesis revisitedIndian dental academy
 
Functional matrix revisited /certified fixed orthodontic courses by Indian...
Functional matrix revisited    /certified fixed orthodontic courses by Indian...Functional matrix revisited    /certified fixed orthodontic courses by Indian...
Functional matrix revisited /certified fixed orthodontic courses by Indian...Indian dental academy
 
Standard Deviation
Standard DeviationStandard Deviation
Standard DeviationJRisi
 
Null hypothesis for a Chi-Square Test of Independence
Null hypothesis for a Chi-Square Test of IndependenceNull hypothesis for a Chi-Square Test of Independence
Null hypothesis for a Chi-Square Test of IndependenceKen Plummer
 
Chi-Square Test of Independence
Chi-Square Test of IndependenceChi-Square Test of Independence
Chi-Square Test of IndependenceKen Plummer
 
The chi – square test
The chi – square testThe chi – square test
The chi – square testMajesty Ortiz
 
Chi square test final
Chi square test finalChi square test final
Chi square test finalHar Jindal
 
mathematical models for drug release studies
mathematical models for drug release studiesmathematical models for drug release studies
mathematical models for drug release studiesSR drug laboratories
 
regression and correlation
regression and correlationregression and correlation
regression and correlationPriya Sharma
 

Viewers also liked (20)

Chi square test
Chi square testChi square test
Chi square test
 
Chi Square Worked Example
Chi Square Worked ExampleChi Square Worked Example
Chi Square Worked Example
 
Null hypothesis for a chi-square goodness of fit test
Null hypothesis for a chi-square goodness of fit testNull hypothesis for a chi-square goodness of fit test
Null hypothesis for a chi-square goodness of fit test
 
Reporting chi square goodness of fit test of independence in apa
Reporting chi square goodness of fit test of independence in apaReporting chi square goodness of fit test of independence in apa
Reporting chi square goodness of fit test of independence in apa
 
Reporting Chi Square Test of Independence in APA
Reporting Chi Square Test of Independence in APAReporting Chi Square Test of Independence in APA
Reporting Chi Square Test of Independence in APA
 
Student t-test
Student t-testStudent t-test
Student t-test
 
Tests of significance
Tests of significanceTests of significance
Tests of significance
 
Analysis of variance (ANOVA)
Analysis of variance (ANOVA)Analysis of variance (ANOVA)
Analysis of variance (ANOVA)
 
Functional matrix hypothesis revisited
Functional matrix hypothesis   revisitedFunctional matrix hypothesis   revisited
Functional matrix hypothesis revisited
 
Functional matrix revisited /certified fixed orthodontic courses by Indian...
Functional matrix revisited    /certified fixed orthodontic courses by Indian...Functional matrix revisited    /certified fixed orthodontic courses by Indian...
Functional matrix revisited /certified fixed orthodontic courses by Indian...
 
Freq distribution
Freq distributionFreq distribution
Freq distribution
 
Standard Deviation
Standard DeviationStandard Deviation
Standard Deviation
 
Malhotra15
Malhotra15Malhotra15
Malhotra15
 
Null hypothesis for a Chi-Square Test of Independence
Null hypothesis for a Chi-Square Test of IndependenceNull hypothesis for a Chi-Square Test of Independence
Null hypothesis for a Chi-Square Test of Independence
 
Chi-Square Test of Independence
Chi-Square Test of IndependenceChi-Square Test of Independence
Chi-Square Test of Independence
 
The chi – square test
The chi – square testThe chi – square test
The chi – square test
 
Chi square test final
Chi square test finalChi square test final
Chi square test final
 
mathematical models for drug release studies
mathematical models for drug release studiesmathematical models for drug release studies
mathematical models for drug release studies
 
regression and correlation
regression and correlationregression and correlation
regression and correlation
 
Z And T Tests
Z And T TestsZ And T Tests
Z And T Tests
 

Similar to Chi square test

Parametric & non parametric
Parametric & non parametricParametric & non parametric
Parametric & non parametricANCYBS
 
Chi square test
Chi square testChi square test
Chi square testNayna Azad
 
Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOUInferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOUEqraBaig
 
Chisquare Test of Association.pdf in biostatistics
Chisquare Test of Association.pdf in biostatisticsChisquare Test of Association.pdf in biostatistics
Chisquare Test of Association.pdf in biostatisticsmuhammadahmad00495
 
Lect w7 t_test_amp_chi_test
Lect w7 t_test_amp_chi_testLect w7 t_test_amp_chi_test
Lect w7 t_test_amp_chi_testRione Drevale
 
chi-Square. test-
chi-Square. test-chi-Square. test-
chi-Square. test-shifanaz9
 
CHI SQUARE TEST by Katha Sanyal
CHI SQUARE TEST by Katha SanyalCHI SQUARE TEST by Katha Sanyal
CHI SQUARE TEST by Katha SanyalKatha Sanyal
 
36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx
36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx
36086 Topic Discussion3Number of Pages 2 (Double Spaced).docxrhetttrevannion
 
Statistical techniques used in measurement
Statistical techniques used in measurementStatistical techniques used in measurement
Statistical techniques used in measurementShivamKhajuria3
 
Chi square test presentation
Chi square test presentationChi square test presentation
Chi square test presentationMD ASADUZZAMAN
 
Non parametrics tests
Non parametrics testsNon parametrics tests
Non parametrics testsrodrick koome
 
Categorical data final
Categorical data finalCategorical data final
Categorical data finalMonika
 

Similar to Chi square test (20)

Chisquare
ChisquareChisquare
Chisquare
 
Parametric & non parametric
Parametric & non parametricParametric & non parametric
Parametric & non parametric
 
Chi square
Chi square Chi square
Chi square
 
Busniess stats
Busniess statsBusniess stats
Busniess stats
 
Chi square test
Chi square testChi square test
Chi square test
 
Contingency tables
Contingency tables  Contingency tables
Contingency tables
 
Chi square test
Chi square testChi square test
Chi square test
 
Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOUInferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
 
Chisquare Test of Association.pdf in biostatistics
Chisquare Test of Association.pdf in biostatisticsChisquare Test of Association.pdf in biostatistics
Chisquare Test of Association.pdf in biostatistics
 
Lect w7 t_test_amp_chi_test
Lect w7 t_test_amp_chi_testLect w7 t_test_amp_chi_test
Lect w7 t_test_amp_chi_test
 
Contingency Tables
Contingency TablesContingency Tables
Contingency Tables
 
chi-Square. test-
chi-Square. test-chi-Square. test-
chi-Square. test-
 
CHI SQUARE TEST by Katha Sanyal
CHI SQUARE TEST by Katha SanyalCHI SQUARE TEST by Katha Sanyal
CHI SQUARE TEST by Katha Sanyal
 
36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx
36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx
36086 Topic Discussion3Number of Pages 2 (Double Spaced).docx
 
Statistical techniques used in measurement
Statistical techniques used in measurementStatistical techniques used in measurement
Statistical techniques used in measurement
 
Chi square test presentation
Chi square test presentationChi square test presentation
Chi square test presentation
 
Design of experiments(
Design of experiments(Design of experiments(
Design of experiments(
 
Chi square
Chi squareChi square
Chi square
 
Non parametrics tests
Non parametrics testsNon parametrics tests
Non parametrics tests
 
Categorical data final
Categorical data finalCategorical data final
Categorical data final
 

More from Patel Parth

Automated analysis by yatin sankharva copy
Automated analysis by yatin sankharva   copyAutomated analysis by yatin sankharva   copy
Automated analysis by yatin sankharva copyPatel Parth
 
Automated analysis 112070804013
Automated analysis 112070804013Automated analysis 112070804013
Automated analysis 112070804013Patel Parth
 
Anda registration in us eu
Anda registration in us  euAnda registration in us  eu
Anda registration in us euPatel Parth
 
Analytical tech in pre formulation 112070804009
Analytical tech in pre formulation 112070804009Analytical tech in pre formulation 112070804009
Analytical tech in pre formulation 112070804009Patel Parth
 
Analysis of solid oral
Analysis of solid oralAnalysis of solid oral
Analysis of solid oralPatel Parth
 
Analysis of solid oral dosage forms 112070804010
Analysis of solid oral dosage forms 112070804010Analysis of solid oral dosage forms 112070804010
Analysis of solid oral dosage forms 112070804010Patel Parth
 
Analysis of parenteral dosage forms bjl final seminar
Analysis of parenteral dosage forms bjl final seminarAnalysis of parenteral dosage forms bjl final seminar
Analysis of parenteral dosage forms bjl final seminarPatel Parth
 
Analysis of data (pratik)
Analysis of data (pratik)Analysis of data (pratik)
Analysis of data (pratik)Patel Parth
 
Analysis of cosmetics 112070804018
Analysis of cosmetics 112070804018Analysis of cosmetics 112070804018
Analysis of cosmetics 112070804018Patel Parth
 
A seminar on applications of various analytical technique
A seminar on applications of various analytical techniqueA seminar on applications of various analytical technique
A seminar on applications of various analytical techniquePatel Parth
 
23117 copy of oral solid dosage forms
23117 copy of oral solid dosage forms23117 copy of oral solid dosage forms
23117 copy of oral solid dosage formsPatel Parth
 
4016 solid state analysis
4016 solid state analysis4016 solid state analysis
4016 solid state analysisPatel Parth
 
4003 regulatory aspect_of_bulk,pharmaceutical,biotech
4003 regulatory aspect_of_bulk,pharmaceutical,biotech4003 regulatory aspect_of_bulk,pharmaceutical,biotech
4003 regulatory aspect_of_bulk,pharmaceutical,biotechPatel Parth
 
A.a sequence analysis 112070804002
A.a sequence analysis 112070804002A.a sequence analysis 112070804002
A.a sequence analysis 112070804002Patel Parth
 
Sterility testing 112070804014
Sterility testing 112070804014Sterility testing 112070804014
Sterility testing 112070804014Patel Parth
 
Ria 112070804007
Ria 112070804007Ria 112070804007
Ria 112070804007Patel Parth
 
Qc lab 112070804001
Qc lab 112070804001Qc lab 112070804001
Qc lab 112070804001Patel Parth
 
Pyrogen testing 112070804005
Pyrogen testing  112070804005Pyrogen testing  112070804005
Pyrogen testing 112070804005Patel Parth
 

More from Patel Parth (20)

Automated analysis by yatin sankharva copy
Automated analysis by yatin sankharva   copyAutomated analysis by yatin sankharva   copy
Automated analysis by yatin sankharva copy
 
Automated analysis 112070804013
Automated analysis 112070804013Automated analysis 112070804013
Automated analysis 112070804013
 
Anda registration in us eu
Anda registration in us  euAnda registration in us  eu
Anda registration in us eu
 
Anda ppt
Anda pptAnda ppt
Anda ppt
 
Analytical tech in pre formulation 112070804009
Analytical tech in pre formulation 112070804009Analytical tech in pre formulation 112070804009
Analytical tech in pre formulation 112070804009
 
Analysis of solid oral
Analysis of solid oralAnalysis of solid oral
Analysis of solid oral
 
Analysis of solid oral dosage forms 112070804010
Analysis of solid oral dosage forms 112070804010Analysis of solid oral dosage forms 112070804010
Analysis of solid oral dosage forms 112070804010
 
Analysis of parenteral dosage forms bjl final seminar
Analysis of parenteral dosage forms bjl final seminarAnalysis of parenteral dosage forms bjl final seminar
Analysis of parenteral dosage forms bjl final seminar
 
Analysis of data (pratik)
Analysis of data (pratik)Analysis of data (pratik)
Analysis of data (pratik)
 
Analysis of cosmetics 112070804018
Analysis of cosmetics 112070804018Analysis of cosmetics 112070804018
Analysis of cosmetics 112070804018
 
Agencies dhwani
Agencies dhwaniAgencies dhwani
Agencies dhwani
 
A seminar on applications of various analytical technique
A seminar on applications of various analytical techniqueA seminar on applications of various analytical technique
A seminar on applications of various analytical technique
 
23117 copy of oral solid dosage forms
23117 copy of oral solid dosage forms23117 copy of oral solid dosage forms
23117 copy of oral solid dosage forms
 
4016 solid state analysis
4016 solid state analysis4016 solid state analysis
4016 solid state analysis
 
4003 regulatory aspect_of_bulk,pharmaceutical,biotech
4003 regulatory aspect_of_bulk,pharmaceutical,biotech4003 regulatory aspect_of_bulk,pharmaceutical,biotech
4003 regulatory aspect_of_bulk,pharmaceutical,biotech
 
A.a sequence analysis 112070804002
A.a sequence analysis 112070804002A.a sequence analysis 112070804002
A.a sequence analysis 112070804002
 
Sterility testing 112070804014
Sterility testing 112070804014Sterility testing 112070804014
Sterility testing 112070804014
 
Ria 112070804007
Ria 112070804007Ria 112070804007
Ria 112070804007
 
Qc lab 112070804001
Qc lab 112070804001Qc lab 112070804001
Qc lab 112070804001
 
Pyrogen testing 112070804005
Pyrogen testing  112070804005Pyrogen testing  112070804005
Pyrogen testing 112070804005
 

Chi square test

  • 2. CONTENTS: •IMPORTANT TERMS •INTRODUCTION •CHARACTERISTICS OF THE TEST •CHI SQUARE DISTRIBUTION •APPLICATIONS OF CHI SQUARE TEST •CALCULATION OF THE CHI SQUARE •CONDITION FOR THE APPLICATION OF THE TEST •EXAMPLE •YATE’S CORRECTION FOR CONTINUITY •LIMITATIONS OF THE TEST.
  • 3. IMPORTANT TERMS 1) PARAMETRIC TEST: The test in which, the population constants like mean,std deviation, std error, correlation coefficient, proportion etc. and data tend to follow one assumed or established distribution such as normal, binomial, poisson etc. 2) NON PARAMETRIC TEST: the test in which no constant of a population is used. Data do not follow any specific distribution and no assumption are made in these tests. E.g. to classify good, better and best we just allocate arbitrary numbers or marks to each category. 3) HYPOTHESIS: It is a definite statement about the population parameters.
  • 4. 4) NULL HYPOTHESIS: (H0) states that no association exists between the two cross-tabulated variables in the population, and therefore the variables are statistically independent. E.g. if we want to compare 2 methods method A and method B for its superiority, and if the assumption is that both methods are equally good, then this assumption is called as NULL HYPOTHESIS. 5) ALTERNATIVE HYPOTHESIS: (H1) proposes that the two variables are related in the population. If we assume that from 2 methods, method A is superior than method B, then this assumption is called as ALTERNATIVE HYPOTHESIS.
  • 5. 6) DEGREE OF FREEDOM: It denotes the extent of independence (freedom) enjoyed by a given set of observed frequencies Suppose we are given a set of n observed frequencies which are subjected to k independent constraints(restrictions) then, d.f. = (number of frequencies) – (number of independent constraints on them) In other terms, df = (r – 1)(c – 1) where r = the number of rows c = the number of columns 7) CONTINGENCY TABLE: When the table is prepared by enumeration of qualitative data by entering the actual frequencies, and if that table represents occurance of two sets of events, that table is called the contingency table. (Latin, con- together, tangere- to touch). It is also called as an association table.
  • 6. INTRODUCTION The chi-square test is an important test amongst the several tests of significance developed by statisticians. Is was developed by Karl Pearson in1900. CHI SQUARE TEST is a non parametric test not based on any assumption or distribution of any variable. This statistical test follows a specific distribution known as chi square distribution. In general The test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis is called the chi-square test.
  • 7. IMPORTANT CHARACTERISTICS OF A CHI SQUARE TEST  This test (as a non-parametric test) is based on frequencies and not on the parameters like mean and standard deviation.  The test is used for testing the hypothesis and is not useful for estimation.  This test can also be applied to a complex contingency table with several classes and as such is a very useful test in research work.  This test is an important non-parametric test as no rigid assumptions are necessary in regard to the type of population, no need of parameter values and relatively less mathematical details are involved.
  • 8. CHI SQUARE DISTRIBUTION: If X1, X2,….Xn are independent normal variates and each is distributed normally with mean zero and standard deviation unity, then X12+X22+……+Xn2= ∑ Xi2 is distributed as chi square (c2 )with n degrees of freedom (d.f.) where n is large. The chi square curve for d.f. N=1,5 and 9 is as follows.
  • 9. If degree of freedom > 2 : Distribution is bell shaped If degree of freedom = 2 : Distribution is L shaped with maximum ordinate at zero If degree of freedom <2 (>0) : Distribution L shaped with infinite ordinate at the origin.
  • 10. APPLICATIONS OF A CHI SQUARE TEST. This test can be used in 1) Goodness of fit of distributions 2) test of independence of attributes 3) test of homogenity.
  • 11. 1) TEST OF GOODNESS OF FIT OF DISTRIBUTIONS:  This test enables us to see how well does the assumed theoretical distribution (such as Binomial distribution, Poisson distribution or Normal distribution) fit to the observed data. The c2 test formula for goodness of fit is: (o  e) 2    2 e Where, o = observed frequency e = expected frequency If c2 (calculated) > c2 (tabulated), with (n-1) d.f, then null hypothesis is rejected otherwise accepted. And if null hypothesis is accepted, then it can be concluded that the given distribution follows theoretical distribution.
  • 12. 2) TEST OF INDEPENDENCE OF ATTRIBUTES Test enables us to explain whether or not two attributes are associated. For instance, we may be interested in knowing whether a new medicine is effective in controlling fever or not, c2 test is useful. In such a situation, we proceed with the null hypothesis that the two attributes (viz., new medicine and control of fever) are independent which means that new medicine is not effective in controlling fever. c2 (calculated) > c2 (tabulated) at a certain level of significancfe for given degrees of freedom, the null hypothesis is rejected, i.e. two variables are dependent.(i.e., the new medicine is effective in controlling the fever) and if, c2 (calculated) <c2 (tabulated) ,the null hypothesis is accepted, i.e. 2 variables are independent.(i.e., the new medicine is not effective in controlling the fever). when null hypothesis is rejected, it can be concluded that there is a significant association between two attributes.
  • 13. 3) TEST OF HOMOGENITY  This test can also be used to test whether the occurance of events follow uniformity or not e.g. the admission of patients in government hospital in all days of week is uniform or not can be tested with the help of chi square test. c2 (calculated) < c2 (tabulated), then null hypothesis is accepted, and it can be concluded that there is a uniformity in the occurance of the events. (uniformity in the admission of patients through out the week)
  • 14. CALCULATION OF CHI SQUARE (o  e) 2    2 e Where, O = observed frequency E = expected frequency If two distributions (observed and theoretical) are exactly alike, c2 = 0; (but generally due to sampling errors, c2 is not equal to zero)
  • 15. STEPS INVOLVED IN CALCULATING c2 1) Calculate the expected frequencies and the observed frequencies: Expected frequencies fe : the cell frequencies that would be expected in a contingency table if the two variables were statistically independent. Observed frequencies fo: the cell frequencies actually observed in a contingency table. fe = (column total)(row total) N To obtain the expected frequencies for any cell in any cross- tabulation in which the two variables are assumed independent, multiply the row and column totals for that cell and divide the product by the total number of cases in the table.
  • 16. 2) Then c2 is calculated as follows: ( fe  fo ) 2 c   2 fe
  • 17. CONDITIONS FOR THE APPLICATION OF c2 TEST The following conditions should be satisfied before X2 test can be applied: 1) The data must be in the form of frequencies 2) The frequency data must have a precise numerical value and must be organised into categories or groups. 3) Observations recorded and used are collected on a random basis. 4) All the itmes in the sample must be independent. 5) No group should contain very few items, say less than 10. In case where the frequencies are less than 10, regrouping is done by combining the frequencies of adjoining groups so that the new frequencies become greater than 10. (Some statisticians take this number as 5, but 10 is regarded as better by most of the statisticians.) 6) The overall number of items must also be reasonably large. It should normally be at least 50.
  • 19.
  • 20. YATE’S CORRECTION If in the 2*2 contingency table, the expected frequencies are small say less than 5, then c2 test can’t be used. In that case, the direct formula of the chi square test is modified and given by Yate’s correction for continuity R1R2C1C2
  • 21. LIMITATIONS OF A CHI SQUARE TEST 1) The data is from a random sample. 2) This test applied in a four fould table, will not give a reliable result with one degree of freedom if the expected value in any cell is less than 5. in such case, Yate’s correction is necessry. i.e. reduction of the mode of (o – e) by half. 3) Even if Yate’s correction, the test may be misleading if any expected frequency is much below 5. in that case another appropriate test should be applied. 4) In contingency tables larger than 2*2, Yate’s correction cannot be applied. 5) Interprit this test with caution if sample total or total of values in all the cells is less than 50.
  • 22. 6) This test tells the presence or absence of an association between the events but doesn’t measure the strength of association. 7) This test doesn’t indicate the cause and effect, it only tells the probability of occurance of association by chance. 8) the test is to be applied only when the individual observations of sample are independent which means that the occurrence of one individual observation (event) has no effect upon the occurrence of any other observation (event) in the sample under consideration.