a borrowed ppt on chi squareanalysis

7/28/2019 a borrowed ppt on chi squareanalysis

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Chi-Square Test ofIndependence

SHAMEER P.H

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REWIND YOUR MIND

Hypothesis-

mere assumption to be proved or disproved

normal question that intends to resolve

tentative formulated for empirical testing

tentative answer to research question

point to start a research


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Research Questions and Hypotheses

Research question: Non-directional:

No stated expectation about outcome

Example:

Do men and women differ in terms of conversational memory? Hypothesis:

Statement of expected relationship Directionality of relationship

Example: Women will have greater conversational memory than men


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The Null Hypothesis

Null Hypothesis - the absence of a relationship

E..g., There is no difference between mens and womenswith regards to conversational memories

Compare observed results to Null Hypothesis

How different are the results from the null hypothesis?

We do not propose a null hypothesis as research

hypothesis - need very large sample size / power Used as point of contrast for testing de

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Hypotheses testing

When we test observed results against null:

We can make two decisions:

1. Accept the null

No significant relationship

Observed results similar to the Null Hypothesis 2. Reject the null

Significant relationship

Observed results different from the Null Hypothesis

Whichever decision, we risk making an error


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Type I and Type II Error

1. Type I Error Reality: No relationship Decision: Reject the null

Believe your research hypothesis have received support when infact you should have disconfirmed it

Analogy: Find an innocent man guilty of a crime

2. Type II Error Reality: Relationship Decision: Accept the null

Believe your research hypothesis has not received support whenin fact you should have rejected the null.

Analogy: Find a guilty man innocent of a crime

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Potential outcomes of testingDecision

Accept Null Reject Null

R NoE RelationshipALITY Relationship

Type II ErrorCorrectdecision

Type I Error

Correct

decision

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Start by setting level of risk of

making a Type I Error How dangerous is it to make a Type I Error:

What risk is acceptable?:

5%?

1%?

.1%?

Smaller percentages are more conservative in guarding against a

Type I Error

Level of acceptable risk is called Significance level :

Usually the cutoff -


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Steps in Hypothesis Testing

1) State research hypothesis

2) State null hypothesis

3) Decide the appropriate test criterion( eg. t test, 2 test, Ftest etc.)

4) Set significance level (e.g., .05 level)

5) Observe results

6) Statistics calculate probability of results if null hypothesiswere true

7) If probability of observed results is less than significancelevel, then reject the null

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Guarding against Errors

Significance level regulates Type I Error

Conservative standards reduce Type I Error:

.01 instead of .05, especially with large sample

Reducing the probability of Type I Error:

Increases the probability of Type II Error

Sample size regulates Type II Error

The larger the sample, the lower the probability of Type II Error

occurring in conservative testingdept.


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Methods used to test

hypothesis

T test

Z test

F test

2 test

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Testing hypothesis for two

nominal variablesVariables Null hypothesis Procedure

Gender

Passing is not Chi-square

related to gender

Pass/Fail

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Testing hypothesis for one

nominal and one ratio variableVariables Null hypothesis Procedure

Gender

Score is not T-test

related to gender

Test score

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Testing hypothesis for one

nominal and one ratio variableVariable Null hypothesis ProcedureYear in school

Score is notrelated to year in ANOVA

schoolTest score

Can be used when nominal variable has more than two categories and can includemore than one independent variable

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Testing hypothesis for two ratio

variablesVariable Null hypothesis Procedure

Hours spent

studying Score is not

related to hours Correlationspent studying

Test score

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Testing hypothesis for more than

two ratio variablesVariable Null hypothesis Procedure

Hours spent

studying Score is positively

related to hours

Classes spent studying and Multiple

missed negatively related regression

to classes missed

Test score

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Chi square (2 ) test

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Used to:

Test for goodness of fit

Test for independence of attributes

Testing homogeneity Testing given population variance

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Chi-Square Test of

Independence

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Introduction (1)

We often have occasions to makecomparisons between two characteristicsof something to see if they are linked or

related to each other.

One way to do this is to work out what we

would expect to find if there was norelationship between them (the usual nullhypothesis) and what we actually observe.

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Introduction (2)

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.

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For Example

Some null hypotheses may be:

there is no relationship between the subjectof first period and the number of studentsabsent in our class.

there is no relationship between the height ofthe land and the vegetation cover.

there is no connection between the size offarm and the type of farm

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Important

The chi square test can only be used on data that has the followingcharacteristics:

The data must be in the formof frequencies

The frequency data must have aprecise numerical value and must beorganised into categories or groups.

The total number of observations must begreater than 20.

The expected frequency in any one cellof the table must be greater than 5.dept.


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Degrees of Freedom

no of independent observations

Number of cells no. of constraints

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Formula

2 = (O E)2

E

2 = The value of chi squareO = The observed valueE = The expected value (O E)2 = all the values of (O E) squared then added

together

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Critical region:

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Construct a table with the information you have observedor obtained.

Observed Frequencies (O)

Money Health Love RowTotal

men 82 446 355 883

women 46 574 273 893

Column total 128 1020 628 1776

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For each of the cells calculate.

money health love RowTotal

Men 5.30 7.37 5.85

women 5023 7.29 5.8

Column Total 2Calc. =36.873

(O E)2

E

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2Calc. = sum of all ( O-E)2/ E values in the

cells.

Here 2Calc. =36.873

Find 2critical From the table with degree offreedom 2 and level of significance 0.05

2

Critical =5.99dept.


2

2 table


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2table

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Conclusion

Compare2Calc.and 2critical obtained from the table

If2Calc. Is larger than2Critical.then reject null

hypothesis and accept the alternative

Here since 2

Calc.is much greater than 2

Critical,

we can

easily reject null hypothesis

that is ; there lies a relation between the gender and

choice of selection.

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Reference

RESEARCH METHODOLGIES

- L R Potti

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a borrowed ppt on chi squareanalysis

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