Independence: If the occurrence of one of the factors in a ...
Independence: If the occurrence of one of the factors in a given sample affects the occurrence of the other, then the two factors are not independent of each other.
The χ2 test examines the difference between the ______________________ and ______________________ values.
Part I. Calculating Expected Values:
The following contingency table shows the results of a sample of 400 randomly selected adults classified according to gender and regular exercise.
| |Pets |No Pets |Sum |
|Male | | | |
|Female | | | |
|Sum | | | |
| |Pets |No Pets |Sum |
|Male | | | |
|Female | | | |
|Sum | | | |
Practice – Find the expected values for the following contingency tables.
1. Students who use pencils or pens vs. right-handed or left-handed
Observed Values Expected Values
| |Pencils |Pens |Sum |
|Right- |31 |22 | |
|handed | | | |
|Left- |20 |27 | |
|handed | | | |
| Sum | | | |
The Formal χ2 Test for independence.
Step 1: State the Null Hypothesis (for our class survey)
H0: _________________________ and _____________________ are INDEPENDENT.
The alternative Hypotheis:
H1: _________________________ and _____________________ are NOT INDEPENDENT.
Step 2: Degrees of Freedom
To find the χ2 distribution you must determine the degrees of freedom (df) for each contingency table.
df = (r-1)(c-1) for a contingency table which is r x c in size.
Calculate the df - ___________________________________________________
Step 3: The problem states the significance level
For this problem, let’s say that it is a 5% significance level
Step 4: State the rejection inequality χ2 > k, where k is obtained from the table of critical values.
We reject Ho if ____________________
Step 5: Find χ2using matrices
1) Put Observed values in a 2x2 Matrix A(Note: your calculator automatically finds the
expected values and inserts them into Matrix B)
2) Press STAT , ►, ►, TESTS, go down 3) Press ▼, ▼, to Calculate, Press
to C: χ2 – Test, Press Enter Enter
[pic] [pic]
χ2 = ________________________________
Step 6: If the rejection inequality is true, then we accept H0. If it is not true, then we reject H0.
______________ _______ _______________
χ2 Critical Value
Step 7: Look at p – value. If p > significance level we accept H0. If p < .05, we reject H0.
P = _________________ ___________ .05, which is further evidence to _______________ H0
Step 8: Conclusion
Example : A survey was given to randomly chosen high school students from years 9 to 12 on possible changes to the school’s canteen. The contingency table shows the results. At a 5% level, test whether there is a significant difference between the proportion of students wanting a change in the canteen across the four year groups.
| |9 |10 |11 |12 |
|Change |7 |9 |13 |14 |
|No Change |14 |12 |9 |7 |
Step 1: State H0 – the null hypothesis. This is a statement that the two variables are considered independent.
H0 – ___________________________________________________
Step 2: Calculate the df
df - ___________________________________________________
Step 3: The problem states the significance level ______________________
Step 4: State the rejection inequality χ2 > k, where k is obtained from the table of critical values.
We reject Ho if ____________________
Step 5: Find χ2 using the contingency table and your calculator
Expected values:
χ2 = ________________________________
Step 6: If the rejection inequality is true, then we accept H0. If it is not true, then we reject H0.
______________ __________ _______________
χ2 Critical Value
Step 7: Look at p – value. If p > significance level we accept H0. If p < .05, we reject H0.
P = __________
Step 8: Conclusion:
1. Students who use pencils or pens vs. right-handed or left-handed
Observed Values Expected Values
| |Pencils |Pens |Sum |
|Right- |31 |22 | |
|handed | | | |
|Left- |20 |27 | |
|handed | | | |
| Sum | | | |
Step 1: State H0 – the null hypothesis. This is a statement that the two variables are considered independent.
H0 – ___________________________________________________
Step 2: Calculate the df
df - ___________________________________________________
Step 3: The problem states the significance level ______________________
Step 4: State the rejection inequality χ2 > k, where k is obtained from the table of critical values.
We reject Ho if ____________________
Step 5: Find χ2 using the contingency table and your calculator
Expected values:
χ2 = ________________________________
Step 6: If the rejection inequality is true, then we accept H0. If it is not true, then we reject H0.
______________ __________ _______________
χ2 Critical Value
Step 7: Look at p – value. If p > significance level we accept H0. If p < .05, we reject H0.
P = __________
Step 8: Conclusion:
-----------------------
χ2 = Σ [pic] where[pic]is an observed frequency and [pic]is an expected frequency.
To find the table of expected values:
Step 1: Sum all rows and columns
Step 2: Multiply the sums for each row and column and divide by the lower right corner box.
| |Pencils |Pens |
|Right- | | |
|handed | | |
|Right- | | |
|handed | | |
| |Pencils |Pens |
|Right- | | |
|handed | | |
|Right- | | |
|handed | | |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- the importance of one s name
- she s one of the guys
- if the diameter of circle c
- one of the things synonym
- calculate the energy of one photon
- one of the grammar
- one of the most grammar
- events in chapter one of the outsiders
- one of the kind
- examples of abiotic factors in the ocean
- example of abiotic factors in one ecosystem
- abiotic factors in a rainforest