Practical Connection Assignment
Kishan@1529
ChiSquarepowerpoint.pptxWeek Two
Chi Square Test
Email: [email protected]
Phone: 941-822-1000
Appointment: Call, text, or email
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Statistical Tests:
This chart is available in the week one folder.
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Chi Square
The chi square (pronounced “ki square”)
Symbolized by X 2
The null hypothesis is that the variables are independent.
If we reject, then the variables are related.
Chi square is an old standard test used to compare frequency data such as those that can be converted to percentages. The results of a chi test can tell you whether or not two or more data sets are indeed different. They also tell you whether or not random chance created the differences that seem to exist.
The null hypothesis is the variables are independent. If we reject, then the variables are related.
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Formula
X2 = ∑[(o – E)2 ]
E
where O = observed frequency and E = expected frequency (based on probability).
Expected frequency is the product of the proportion of respective rows and columns.
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Reporting the Chi-Square results
(X2 [ df, N = count] = chi square result, p less than or greater than .05)
(X2 [ 1, N= 140] = 20.54, p< .05)
Report the degrees of freedom, the count, the chi-square statistic, and the significance (p < or > .05)
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What do the Symbols mean?
(X2 [1, N = 140] = 20.54; p < .001)
Critical values, which are found in the Appendix C of Spatz’s book, tell us the level or values that our test statistic needs to equal to show a statistical significance. To find the critical value with which you compare your test statistic, locate on the left hand side the column showing degrees of freedom (df) and then look across the corresponding columns to find the greatest level of significance, if any, and use that alpha (.05, .01, etc.) in reporting your results.
Find Table E, in Appendix C.
If results are significant, variables are related.
Degrees of Freedom
See section in chapter 14
(R-1)(C-1)
In a 2x2, df =1 (2-1)(2-1)=1
In a 3x3, df = 4 (3-1)(3-1)= 4
If the X2 value is smaller than the table, the variables are independent, you accept the null (no relationship between variables). If the X2 value is larger than the value in the table, the variables are not independent. The null is rejected, which means the variables are related. In this case gender and attitude were related.
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An example from a dissertation:
The researcher wanted to explore the amount of training received by administrators and teachers and to explore the need for training in the area. Seventy-six percent (N = 26) of administrators reported participation in training, while 52 percent (N = 101) of teachers reported participation in training. A chi-square test was conducted to determine if there was a relationship between the participants’ position (teacher or administrator) and training (received or not received). It was determined that there is a relationship between the participants position and training received at the .05 level, (χ2 [1, N= 127] = 5.06, p < 0.05).
Since the p value is less than .05, we reject the null hypothesis that these variables are independent. In this case, position and training were related.
Page 304.
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2x2 Example
Let’s look at an example that involves gender and product placement.
In a store, items were either placed in proximity to similar items, or with items that may be used together.
For example, sun hats placed with baseball caps (similar items) as opposed to sun hats placed with sunscreen (items that may be used together).
Eighty eight females and 52 males participated in the study.
Fifty nine females purchased similarly placed items, and 15 males purchased similarly placed items.
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Using the Chi-Square
Chi Square can help us answer the following:
Are females more likely to purchase similarly placed products?
How can we make a clearly objective statement about their any relationship?
Well, chi square empowers us to determine that in fact gender makes a difference in product placement.
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Calculating Expected Values (Rounded):
Observed Values
Expected Values (rounded)
Notice the sums for the observed and expected values match.
Note that expected frequencies can also be calculated by (52)(74)/140 = 27.49, which due to rounding, is slightly higher. Rounding usually produces a slight smaller and more conservative test statistic).
Again, rounding may result in differences that range in the tenths or hundredths. If your results are larger than let’s say 1 or 2 whole numbers, then a mistake was made.
| Similar items | Items used together | Sum | |
| Male | 15 | 37 | 52 |
| Female | 59 | 29 | 88 |
| 74 | 66 | 140 |
| Similar items | Items used together | |
| Male | 27.48571429 | 24.5142857 |
| Female | 46.51428571 | 41.4857143 |
To find expected frequencies we begin by assuming the categories are independent.
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Table for Calculating Chi Square
Here are the values rounded. The X2 is 19.14.
| Observed | Expected | (O-E)2 | (O-E)2 /E | |
| Male Similar | 15 | 27.4857143 | 155.8931 | 5.671785 |
| Male Together | 37 | 24.5142857 | 155.8931 | 6.359274 |
| Female Similar | 59 | 46.5142857 | 155.8931 | 3.351509 |
| Female Together | 29 | 41.4857143 | 155.8931 | 3.757753 |
| X2 | 19.14032 |
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Here is the table from Spatz…
(X2 [1, N = 140] = 20.54; p < .001)
We start at the .05 level looking for significance. Our value is 20.54, that is larger than 3.841. In fact our value is larger than the value at the .001 level.
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3 X 3 Chi Square
Suppose we want to eliminate chance in a situation in which prison, high school, and college faculty selected their preferred class size: Small class less than 15 students; medium sized classes 16-30 students, and large classes 31 to 45 students.
Prison faculty: 61, 38, 18 = 117
High school: 26, 57, 9
College: 17, 35, 14
Is there a difference in the way prison teachers, 7-12, and college instructors view ideal class sizes?
Please perform the test.
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Open the chi-square calculator template
Step 1:
Select the 3x3 template
Step 2:
Enter the observed values
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The results:
Step 3:
Find the chi-square value and determine the significance.
Note that 6.11705E-05 is scientific notation for a value of .0000611705
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