Statistical Analysis for IB Psychology. The chi-square test is a method of statistical analysis used for comparison of observed/ actual data to expected data.

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Chi-Square Test

The chi-square test is a method of statistical analysis used for comparison of observed/ actual data to expected data. Chi-squared asks and answers the question, “Does my observed data fit with my expectations?”. It is measured as the probability for your event to occur, p> .05 or p<.05. The higher your x2 (chi-square) value, the less likely your results are accurate (or due to chance). The lower the value, the more accurate, or likely to occur.

Example:


A restaurant owner expects that over the course of 6 days, 10% will come in on Monday, 10% on Tuesday, 15% on Wednesday, 20%on Thursday, 30% on Friday, and 15% on Saturday. This is his ‘Expected distribution’.

The null hypothesis would be that:
H
0= The owner’s distribution is correct
and the alternative hypothesis would be:
H1= The owner’s distribution is incorrect

We want to accept or refute the null using the significance of σ =.05, or 5%, to see what the probability of getting a result of this, or more extreme (p<.05), would be.

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He observes that 30 people came in on Monday, 14 on Tuesday, 34 on Wednesday, 45 on Thursday, 57 on Friday, and 20 on Saturday.
We will assume the owners distribution is correct.

Total of 200 Customers throughout the week.

Chi-Square Statistic = χ2
To find this, you would take the (Observed Value - Expected Number) squared, and divide all by the Expected number and do this for each one of your values

So,
χ2 = (30-20)2/20 + (14-20) 2/20 + (34-30) 2/30 + (45-40) 2/40 + (57-60) 2/60 + (20-30) 2/30
χ2= 100/20 + 36/20 + 16/30 + 25/40 + 9/60 + 100/30

χ2 = ...

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