Download - Reasoning in Psychology Using Statistics Psychology 138 2015

Reasoning in PsychologyUsing Statistics

Psychology 138

2015

Reasoning in Psychology Using

Statistics

Annoucements

• Don’t forget quiz 8 due this Friday


Statistics

Chi-Square Test for Independence

A manufacturer of watches takes a sample of 200 people. Each person isclassified by age and watch type preference (digital vs. analog).

A manufacturer of watches takes a sample of 200 people. Each person isclassified by age and watch type preference (digital vs. analog).

The question: Is there a relationship between age and watch preference?

Young (under 30)

Old (over 30)


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Decision tree

• Chi-square test of independence (χ2 lower-case chi )– Describing the relationship between two categorical

variables

or Young Oldor


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A manufacturer of watches takes a sample of 200 people. Each person isclassified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference?


Chi-Squared Test for Independence


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Step 1: State the hypotheses and select an alpha level – H0: Preference is

independent of age (“no relationship”)

– HA: Preference is related to age (“there is a relationship”)

– We’ll set α = 0.05



Observed scores


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Step 2: Compute your degrees of freedom & get critical value

df = (#Columns - 1) * (#Rows - 1)

= (3-1) * (2-1) = 2

• For this example, with df = 2, and α = 0.05


• The critical chi-squared value is 5.99

– Go to Chi-square statistic table and find the critical value


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X2 α = .055.997.81

11.0714.07

As df gets larger, need larger X2 value for significance. Number of cells get larger.


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Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies


Observed scores


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Observed scores

Spot check: make sure the row totals and column totals add up to the same thing


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Under 30

Over 30

Digital Analog Undecided

70 56 14

30 24 6

Observed scores

Expected scores

Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell)


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Under 30

Over 30

Digital Analog Undecided

70 56 14

30 24 6

Observed scores

Expected scores


“expected frequencies” - if the null hypothesis is correct, then these are the frequencies that

you would expect

“expected frequencies” - if the null hypothesis is correct, then these are the frequencies that

you would expect


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• Find the residuals (fo - fe) for each cell

Step 4: compute the χ2



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Computing the Chi-square




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• Square these differences




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• Divide the squared differences by fe




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• Divide the squared differences by fe

• Sum the results



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Chi-Squared, the final step

Step 5: Compare this computed statistic (38.09) against the critical value (5.99) and make a decision about your hypotheses



here we reject the H0 and conclude that there is a relationship between age and watch preference


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Chi square as a statistical test

each cell = observed difference . difference expected by chance


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Chi-Square Test in SPSS

Analyze Descriptives Crosstabs


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Analyze Descriptives Crosstabs

Click this to get the expected frequencies and residuals

Click this to get bar chart of the results


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Wrap up

• In lab: Gain experience using and interpreting Chi-square procedures

• Questions?

Download - Reasoning in Psychology Using Statistics Psychology 138 2015

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