chi square tests (part 3)

8/3/2019 Chi Square Tests (Part 3)

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(Non-Parametric Techniques) Chi-Square Test (2

) (PART 3)

(DR SEE KIN HAI)Fisher's exact test[1][2][3] is a statistical significance test used in the analysis of contingency tables.

Although in the practice it is employed when sample sizes are small, it is valid for all sample sizes. It is

named after its inventor, R. A. Fisher, and is one of a class ofexact tests, so called because thesignificance of the deviation from anull hypothesis can be calculated exactly, rather than relying on an

approximation that becomes exact in the limit as the sample size grows to infinity, as with manystatistical tests.

Fisher Exact Test (Test of Independence / Relatedness) for min expected f < 5

1. You use chi-square procedure to compute Fishers exact test for 2 x 2 tables when one or moreof the cells has expected frequency < 5.

Table shows the number of students from a small school and their preference in games.

Game A Game B

Males 2 7

Females 4 1

Test your Null hypothesis that the two variables (sex and games) are independent of each other.

(OR) That the type of games preferred is not related to students gender.

2. Enter the data into SPSS 20.

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1=Male, 2=Female

1= Game A, 2 = Game B
http://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-0http://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-1http://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-2http://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-2http://en.wikipedia.org/wiki/Statistical_significancehttp://en.wikipedia.org/wiki/Contingency_tablehttp://en.wikipedia.org/wiki/Sample_(statistics)http://en.wikipedia.org/wiki/Ronald_Fisherhttp://en.wikipedia.org/wiki/Exact_testhttp://en.wikipedia.org/wiki/Exact_testhttp://en.wikipedia.org/wiki/Null_hypothesishttp://en.wikipedia.org/wiki/Null_hypothesishttp://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-0http://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-1http://en.wikipedia.org/wiki/Fisher's_exact_test#cite_note-2http://en.wikipedia.org/wiki/Statistical_significancehttp://en.wikipedia.org/wiki/Contingency_tablehttp://en.wikipedia.org/wiki/Sample_(statistics)http://en.wikipedia.org/wiki/Ronald_Fisherhttp://en.wikipedia.org/wiki/Exact_testhttp://en.wikipedia.org/wiki/Null_hypothesis


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3. You have to tell SPSS 20 to count only the [Frequency] by selecting [Data] on the menu bar, then

click on [Weight Cases]

4. Click on [Weight cases by] and move [Frequency] into the [Frequency Variable] box then [OK]

5. Select [Analyze] then [Descriptive Statistics] and [Crosstabs]6. Move [Sex] into [Rows] and [Games] into [Columns] box then select [Statistics] to open the

dialogue box.

7. Select [Chi-square] then [Continue] . The previous screen reappears, select [Cells] to open the

sub-dialogue box.

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8. Now click on [Continue] and [OK] on the previous screen that reappears.

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Interpreting the output for Fishers Exact Chi-Square Test

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This table shows the

observed [Count] and[Expected Count]

frequencies of the 4 cells

Fishers Exact Test = 0.091 at 2-tailed level and 0.063

at 1-tailed level >p = 0.05 thus not significant


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Reporting the output for Fishers exact test

1. There was no significant relationship between sex and the types of games (two-tailed Fisher

exact p = 0.091) or Males and females students do not differ in the frequency of the types of

games they prefer (two-tailed Fisher exact p = 0.091).

2. Care must be taken as the sample size is small. The finding can be considered as marginally

significant and it is recommended that further studies should be done to establish with morecertainty if gender did differ in their games preference.

COURSEWORK

The table shows the types of subjects that are favoured by a sample of 104 students from a school.

You are to find out if gender and the choice of the three subjects are independent of each other. (As

one of the cells has a frequency < 5 , use Fishers exact test)

Respondents Subject A Subject B Subject C

Boys 27 4 19Girls 17 33 4

___________________________________________________________

McNemars Chi-Square Test for 2 related samples

In statistics,McNemar's test is a non-parametric method used on nominal data (see L26). It is applied

to 2 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determinewhether the row and column marginal frequencies are equal ("marginal homogeneity"). It is named

after Quinn McNemar, who introduced it in 1947.[1] An application of the test in genetics is the

transmission disequilibrium test for detecting genetic linkage.[2]

The test is applied to a 2 2 contingency table, which tabulates the outcomes of two tests on a sample

ofn subjects, as follows.

Test 2 positive Test 2 negative Row total

Test 1 positive a b a + b

Test 1 negative c d c + d

Column total a + c b + d n

The null hypothesisof marginal homogeneity states that the two marginal probabilities for eachoutcome are the same, i.e.pa +pb =pa +pc andpc +pd=pb +pd.

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http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Non-parametrichttp://en.wikipedia.org/wiki/Nominal_datahttp://en.wikipedia.org/wiki/Contingency_tablehttp://en.wikipedia.org/wiki/Dichotomoushttp://en.wikipedia.org/wiki/Dichotomoushttp://en.wikipedia.org/wiki/Quinn_McNemarhttp://en.wikipedia.org/wiki/McNemar's_test#cite_note-McNemar1947-0http://en.wikipedia.org/wiki/Transmission_disequilibrium_testhttp://en.wikipedia.org/wiki/McNemar's_test#cite_note-Spielman93-1http://en.wikipedia.org/wiki/Null_hypothesishttp://en.wikipedia.org/wiki/Null_hypothesishttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Non-parametrichttp://en.wikipedia.org/wiki/Nominal_datahttp://en.wikipedia.org/wiki/Contingency_tablehttp://en.wikipedia.org/wiki/Dichotomoushttp://en.wikipedia.org/wiki/Quinn_McNemarhttp://en.wikipedia.org/wiki/McNemar's_test#cite_note-McNemar1947-0http://en.wikipedia.org/wiki/Transmission_disequilibrium_testhttp://en.wikipedia.org/wiki/McNemar's_test#cite_note-Spielman93-1http://en.wikipedia.org/wiki/Null_hypothesis


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Thus the null and alternative hypotheses are[1]

Herepa, etc., denote the theoretical probability of occurrences in cells with the corresponding label.

The McNemartest statisticis:

Summary (Practice)1. Use for 2 x 2 contingency tables with a dichotomous trait (Yes/No or Right/Wrong or

Positive/Negative respond).

2. It is used to test the difference between paired samples and must be mutually independent pairs.

The table below shows the number of Sixth Form students from a school who changed or did not

change their minds about taking Biology after listening to a careers talk by you as the Biology

teacher. The table gives the numbers who wanted to take Biology before the talk and after it (30),those who wanted to take Biology before the talk but not after it (10), those who wanted to take

Biology after the talk but not before it (50), and the numbers not wanting to take Biology both

before and after the talk (32). You are to determine if there was a significant increase in the

number of students taking your Biology subject after your talk.

. 1 Before your talk (yes) 2 Before your talk (no)

1 After talk (yes) 30 502 After talk (no) 10 32

______________________________________________________________________

1. Enter the [Variable view] as below.

2. Enter the data in the [Data View]

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1=Yes 2=No
http://en.wikipedia.org/wiki/McNemar's_test#cite_note-McNemar1947-0http://en.wikipedia.org/wiki/Test_statistichttp://en.wikipedia.org/wiki/Test_statistichttp://en.wikipedia.org/wiki/McNemar's_test#cite_note-McNemar1947-0http://en.wikipedia.org/wiki/Test_statistic


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3. Click on [Data] on the menu bar then [Weight Cases]

4. Select [Analyze] then [Nonparametric Tests] to select [2 Related Samples]

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Select [Weight cases by]

and move [Frequency] in

this box then [OK]


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5. Select [Fields] and move [Before] and [After] into [Test Fields] then click on [Run]

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Interpreting the output for a McNemar chi-square test

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Double click on this box to getthe Table below

The number changes from wanting to

take Biology 30 to 10 after teacher talk

The number changes from not takingBiology (32) to 50 after teacher talk

Total number of cases N=122, chi-

square= 25.350 at sig levelp = 0.000

as this is < 0.05

This indicates that there has been asignificant change in the number of

students taking Biology after teacher

talk.


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Reporting the output for a McNemar Chi-square Test

There was a significant increase in the number of students taking Biology after the teacher had given a

talk to students.

COURSEWORK

The table shows the number of students who have taken a test in Oral English. A total of 100 students

from a school are each assessed with grades of either a pass (1) or Fail (0). Variable A can be defined

as students grade before the training in their oral and Variable B can be defined as students gradeafter they have their training. You are to determine if the training in Oral English increases the number

of student who passes.

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chi square tests (part 3)

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