Chapter 4: Local integration 1: Reasoning & evolutionary psychology
Reasoning in Psychology Using Statistics Psychology 138 2015.
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Transcript of Reasoning in Psychology Using Statistics Psychology 138 2015.
Reasoning in Psychology Using
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)
Reasoning in Psychology Using
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)
Reasoning in Psychology Using
Statistics
Decision tree
• Chi-square test of independence (χ2 lower-case chi )– Describing the relationship between two categorical
variables
or Young Oldor
Reasoning in Psychology Using
Statistics
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?
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
Reasoning in Psychology Using
Statistics
Chi-Squared Test for Independence
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
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?
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?
Observed scores
Reasoning in Psychology Using
Statistics
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
Chi-Squared Test for Independence
• The critical chi-squared value is 5.99
– Go to Chi-square statistic table and find the critical value
Reasoning in Psychology Using
Statistics
Chi-Squared Test for Independence
X2 α = .055.997.81
11.0714.07
As df gets larger, need larger X2 value for significance. Number of cells get larger.
Reasoning in Psychology Using
Statistics
Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies
Chi-Squared Test for Independence
Observed scores
Reasoning in Psychology Using
Statistics
Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies
Chi-Squared Test for Independence
Observed scores
Spot check: make sure the row totals and column totals add up to the same thing
Reasoning in Psychology Using
Statistics
Chi-Squared Test for Independence
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)
Reasoning in Psychology Using
Statistics
Chi-Squared Test for Independence
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
“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
Reasoning in Psychology Using
Statistics
• Find the residuals (fo - fe) for each cell
Step 4: compute the χ2
Chi-Squared Test for Independence
Reasoning in Psychology Using
Statistics
Computing the Chi-square
• Find the residuals (fo - fe) for each cell
Step 4: compute the χ2
Reasoning in Psychology Using
Statistics
Computing the Chi-square
• Square these differences
• Find the residuals (fo - fe) for each cell
Step 4: compute the χ2
Reasoning in Psychology Using
Statistics
Computing the Chi-square
• Find the residuals (fo - fe) for each cell
• Divide the squared differences by fe
Step 4: compute the χ2
• Square these differences
Reasoning in Psychology Using
Statistics
Computing the Chi-square
• Square these differences
• Find the residuals (fo - fe) for each cell
• Divide the squared differences by fe
• Sum the results
Step 4: compute the χ2
Reasoning in Psychology Using
Statistics
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
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?
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?
here we reject the H0 and conclude that there is a relationship between age and watch preference
Reasoning in Psychology Using
Statistics
Chi square as a statistical test
each cell = observed difference . difference expected by chance
Reasoning in Psychology Using
Statistics
Chi-Square Test in SPSS
Analyze Descriptives Crosstabs
Click this to get the expected frequencies and residuals
Click this to get bar chart of the results