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### Transcript of Chi Square report.pptx

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John Henry O. Valencia, RN, RM, MANc

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We often have occasions to make comparisons between two

characteristics of something to see if they are linked or related to each

other.

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One way to do this is to work out what we would expect to find if there

was no relationship between them (the usual null hypothesis) and what

we actually observe.

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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First and foremost, make sure you pronounce it

correctly, chi-square as in kite NOT chee as

in cheetah (Chee-Square?) or chaye as in ChaiTea (Chai-Square?)

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Test for goodness of fit

Test for independence of attributes

Testing homogeneity

Testing given population variance

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Identifies significant differences among

the observed frequencies and the expected

frequencies of a particular group.

Do the number of individuals or objects that fall in each category differ

from the number you would expect?

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Attempts to identify whether any differences

between the expected and observed

frequencies are due to chance, or some

other factor that is affecting it.

Is this difference between the expected and observed are due to sampling

error, or is it a REALdifference?

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Data- 2 types

Numerical data- in form of numbers. (ex.

1,2,3,4) Categorical data- comes in form of divisions.

(ex. Yes or no)

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Observed Frequencies the observed frequencies are the frequencies actually

obtained in each cell of the table, from our random sample.

When conducting a chi-squared test, the term observed

frequencies is used to describe the actual data in the

contingency table.

Observed frequencies are compared with the expectedfrequencies and differences between them suggest that the

model expressed by the expected frequencies does not

describe the data well.

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Expected Frequencies

values for parameters that are hypothesized to

occur

are the frequencies that you would predict

('expect') in each cell of the table, if you knew

only the row and column totals, and if you

assumed that the variables under comparison

were independent.

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can be determined through:

a) Hypothesizing that the frequencies are equal for

each category.

b) Hypothesizing the values on the basis of some

prior knowledge.

c) A mathematical method

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Contingency Tables Frequency table in which a sample from a population is classified

according to two attributes, which are divided in to two or more

classes .

A contingency table is used to summarise categorical data. It may beenhanced by including the percentages that fall into each category.

What you find in the rows of a contingency table is contingent upon

(dependent upon) what you find in the columns.

Can be:

2 x 2

h x k

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Chi-square test for Independence

-This tests whether the categoryfrom which the data comes from

affects the data.

-May also be thought of as testing whether the categories in the

experiment prefercertain kinds of data.

Example: Is there a difference in the car choices of male andfemales?

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Chi-square test for goodness-of-fit

-This tests whether the observeddata fitthe expecteddata.

Example: Do the car sales this year match the car sales last year?

(ie. Did we still sell around 50 blue cars? 25 red cars?)

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The values of the parameters to be compared are

quantitative and nominal.

There should be one or more categories in the setup.

The observations should be independent of each other.

An adequate sample size. (At least 10)

Most of the time, it is the frequency of the observations

that are used.

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Simple random sample

All observations must be used

The expected frequency in any one cell of thetable must be greater than 5.

The total number of observations must be

greater than 20.

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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 addedtogether

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1. State the hypotheses

2. State the level of significance

3. Set up a contingency table

4. Compute for the expected frequencies

5. Rearrange the table to show the observed and expected frequencies

on the columns

6. Determine the degree of freedom

7. Check the tabular Chi-squared value with your df and level of

significance

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A Nutrition and Dietetics Student wants to see whether the food

preferences of males and females differed. He tried to see whether males

or females had a general difference in the preference for cooked and raw

foods. A survey was conducted with the following results:

Twelve males preferred Cooked foods.

Eight males preferred Raw foods.

Five females preferred Cooked foods.

Five females preferred Caw foods.

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H0: There is no significant difference between the food

preferences of males and females. / Food preference is

independent of gender.

H1: There is a significant difference between the food

preferences of males and females. / Food preference is

affected by gender.

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= 0.05

0.05 is the level of significance for mostscientific experiments.

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The contingency table summarizes the data.

The categories on the columns are the preferencesthat you are checking.

The categories on the rows are the populationswhose preferences are being

checked. A row total and column total is always included as well.

Preference Male Female Total (Row)

Cooked 12 5 17

Raw 8 5 13

Total (Column) 20 10 30

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The chi-square test for independence usually uses the third method of getting

expected frequencies.

Expected Frequency = (Row Total)(Column Total)

Grand total

This expected frequency is computed for EACH cell.

Preference Male Female Total (Row)

Cooked (20)(17)/30 =11.33 (10)(17)/30 =5.67 17

Raw (13)(20)/30 =8.67

(13)(10)/30 =4.33

13

Total (Column) 20 10 30

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Preference O E (O-E) (O-E)2 (O-E)2

E

Cooked Male 12 11.33 0.67 0.4489 0.0396

Cooked Female 5 5.67 -0.67 0.4489 0.0792

Raw Male 8 8.67 -0.67 0.4489 0.518

Raw Female 5 4.33 0.67 0.4489 0.1037

Total 0.2743

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The degrees of freedom is:

df = (Rows 1)(Columns 1)

df = (21)(2

1) = 1

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Checking the table, we see that the tabular

chi-squared value for df = 1, and = 0.05 is

3.841.

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Since our calculated chi-square is less than this, the

conclusion is to ACCEPT THE NULL HYPOTHESIS.

Hence, food preference is independent of gender.

If it were greater, we would reject the null hypothesis.

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Coding in SPSS:

Preference Male

(1)

Female

(2)

Total (Row)

Cooked

(1)

12 5 17

Raw

(2)

8 5 13

Total (Column) 20 10 30

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A hospital employs a number of visiting surgeons to undertake

particular operations. If complications occur during or after the operation

the patient has to be transferred to a larger hospital nearby where the

required back up facilities are available.

A hospital administrator, worried by the effects of this on costs,

examines the records of the three surgeons. Surgeon A had 6 out of her

last 47 patients were transferred, Surgeon B, 4 out of his last 72 patients

and surgeon C, 14 out of his last 41.

Form the data into a 2 x 3 contingency table and test at the 5%

significance level, whether the proportion transferred is independent of

the surgeon.

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H0: Patient transfer is independent of surgeons choice

or there is no association on transfer rate and the

surgeon

H1: patient transfer is affected by surgeons choice or

there is an association on transfer rate and the surgeon

Alpha Level:

= 0.05

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SURGEON A B C TOTAL(ROW)

TRANSFERRED 6 4 14 24

NOT-TRANSFERRED 41 68 27 136

Total

(Column)

47 72 41 160

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Since our calculated Chi Square is greater than the

critical value, the conclusion is to reject the null

hypotheses, hence, transfer rate is affected by

surgeonschoice / preference.

The difference between what we expected and our

observation were too great / large to be explained by

Chance alone.

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A marketing firm producing detergents is interested

in studying the consumer behavior in the context ofpurchase decision of detergents in a specific market. It

would like to know in particular whether the income level

of the consumers influence their choice of the brand.

Currently there are two brands in the market. Brand 1 is

the premium brand while Brand 2 is the economy brand.

Income level was classified as Lower, Middle, Upper

Middle and High and random sampling procedure wasadopted covering the entire market. A sample of 300

consumers participated in this study. The following data

emerged from the study.

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Analyze the data using chi-square testand draw your conclusions.

Income Level Brand 1 Brand 2

Lower 25 65Middle 30 30

Upper Middle 50 22

High 60 18

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