The chi-square ((chi^2)) check of freedom is supplied to test because that a relationship in between two categorical variables. Recall that if 2 categorical variables room independent, then (P(A) = P(A mid B)). The chi-square check of independenceuses this reality to compute expected values because that the cell in a two-way contingency table under the assumption that the two variables room independent (i.e., the null theory is true).

You are watching: Which of the following is a basic assumption for a chi-square hypothesis test?

Even if 2 variables are independent in the population, samples will certainly vary as result of random sampling variation. The chi-square check is offered to identify if there is evidence that the two variables space not elevation in the populace using the exact same hypothesis testing logic the we provided with one mean, one proportion, etc.

Again, we will be utilizing the five step hypothesis testing procedure:


1. Check assumptions and also write hypotheses.

The assumptions are that the sample is randomly attracted from the population and the all expected values are at the very least 5 (we will see what meant values space later).

Our hypotheses are:

(H_0:) over there is no a relationship in between the two variables in the populace (they are independent)

(H_a:) there is a relationship between the 2 variables in the population (they aredependent)

Note: as soon as you"re creating the hypotheses for a offered scenario, usage the name of the variables, no the share "two variables."


2. Calculation an ideal test stillproud.orgistic
Chi-Square check stillproud.orgistic(chi^2=sum dfrac(Observed-Expected)^2Expected)
Expected cabinet Value(E=dfracrow;total ; imes ; column;totaln)
3. Determine the p-value

The p-value can be discovered using Minitab. Look up the area to the ideal of your chi-square check stillproud.orgistic top top a chi-square distribution with the correct levels of freedom. Chi-square exam are always right-tailed tests.


Degrees of Freedom: Chi-Square test of Independence(df=(number;of;rows-1)(number;of;columns-1))
4. Do a decision

If (p leq alpha) disapprove the null hypothesis.

If (p>alpha) fail to disapprove the null hypothesis.


5. stillproud.orge a "real world" conclusion

Write a conclusion in regards to the original research question.


11.3.1 - Example: Gender and also stillproud.org learning 11.3.1 - Example: Gender and also stillproud.org finding out

A sample of 314 pen stillproud.orge students was asked if lock have ever before taken an virtual course. Your genders were additionally recorded. The contingency table listed below was constructed. Use a chi-square test of self-reliance to identify if over there is a relationship in between gender and whether or not someone has actually taken an virtual course.

Have you taken an virtual course?YesNoMenWomen
4363
95113

1. Examine assumptions and write hypotheses

(H_0:) over there is no a relationship between gender and also whether or not someone has taken an digital course (they room independent)

(H_a:) over there is a relationship in between gender and also whether or not someone has actually taken an digital course (they space dependent)

Looking front to our calculations of the intended values, we can see the all expected values space at the very least 5. This means that the sampling circulation can be approximated utilizing the (chi^2) distribution. 


2. Calculate the check stillproud.orgistic

In order come compute the chi-square check stillproud.orgistic we must understand the observed and expected values for every cell. Us are given the observed worths in the table above. We should compute the meant values. The table below includes the row and column totals.

 Have you taken an digital course?  YesNo MenWomen
4363106
95113208
 138176314
(E=dfracrow;total imes column;totaln)
(E_Men,;Yes=dfrac106 imes138314=46.586)
(E_Men,;No=dfrac106 imes176314=59.414)
(E_Women,;Yes=dfrac208 imes138314=91.414)
(E_Women,;No=dfrac208 imes 176314=116.586)

Note the all supposed values room at least 5, hence this presumption of the (chi^2) check of independence has been met. 

Observed and also expected counts are often presented with each other in a contingency table. In the table below, supposed values space presented in parentheses.

Have girlfriend taken an stillproud.org course?YesNoMenWomen
  
  
43 (46.586)63 (59.414)106
95 (91.414)113 (116.586)208
 138176314

(chi^2=sum dfrac(O-E)^2E )

(chi^2=dfrac(43-46.586)^246.586+dfrac(63-59.414)^259.414+dfrac(95-91.414)^291.414+dfrac(113-116.586)^2116.586=0.276+0.216+0.141+0.110=0.743)

The chi-square test stillproud.orgistic is 0.743

(df=(number;of;rows-1)(number;of;columns-1)=(2-1)(2-1)=1)


3. Identify the p-value

We have the right to determine the p-value by creating a chi-square circulation plot with 1 level of freedom and finding the area to the right of 0.743.

*

(p = 0.388702)


4. Do a decision

(p>alpha), therefore we fail to refuse the null hypothesis.


5. stillproud.orge a "real world" conclusion

There is not proof that gender and whether or not an individual has actually completed an stillproud.org course space related.

Note that we cannot to speak for sure that these 2 categorical variables room independent, we deserve to only say that we carry out not have evidence that they room dependent.


Research question: Is there a relationship between where a student sits in class and whether lock have ever before cheated?

Null hypothesis: seat location and also cheating are not connected in the population.Alternative hypothesis: seat location and cheating are related in the population.

To perform a chi-square check of independencein Minitab making use of raw data:

Select stillproud.org > Tables > Chi-Square Test because that AssociationSelect Raw data (categorical variables) from the dropdown.Choose the variableSeatingto insert it into theRowsboxChoose the variableEver_Cheatto insert it into theColumnsboxClick the stillproud.orgistics button and also check the boxesChi-square test for associationandExpected cell countsClickOK and OK

This should an outcome in the following output:


Rows: Seating Columns: Ever_CheatNoYesAllBackFrontMiddleAll
24832
24.217.79
38846
34.8111.19
10939148
111.9836.02
171455226
Cell contents:Count
Expected count
Chi-Square TestChi-SquareDFP-ValuePearsonLikelihood Ratio
1.53920.463
1.62620.443

Interpret

All supposed values space at least 5 therefore we can use the Pearson chi-square check stillproud.orgistic. Our outcomes are (chi^2 (2) = 1.539). (p = 0.463). Since our (p) value is better than the typical alpha level of 0.05, us fail to reject the null hypothesis.There is not proof of a relationship in the population between seat location and also whether a student has actually cheated.


Let"s usage Minitab to calculation the test stillproud.orgistic and also p-value.

After entering the data, select stillproud.org > Tables > cross Tabulation and also Chi-SquareEnter Dog in the Rows boxEnter Cat in the Columns boxSelect the Chi-Square button and also in the new window inspect the crate for the Chi-square test and also Expected cabinet countsClickOK and also OKRows: Dog Columns: CatNoYesAllNoYesMissingAll
18369252
176.0275.98
18389272
189.9882.02
10
366158524
Cell contents:
Count
Expected count
Chi-Square TestChi-SquareDFP-ValuePearsonLikelihood Ratio
1.77110.183
1.77510.183

Since the presumption was met in action 1, we deserve to use the Pearson chi-square check stillproud.orgistic.

(Pearson;chi^2 = 1.771)


3. Determine a ns value connected with the test stillproud.orgistic.

(p = 0.183)


4. Decide in between the null and alternative hypotheses.

Our p value is higher than the traditional 0.05 alpha level, so us fail to refuse the null hypothesis.


5. stillproud.orge a "real world" conclusion.

There is not proof of a relationship between dog ownership and also cat ownership in the populace of all civilization Campus stillproud.org 200 students.


Let"s use Minitab to calculate the test stillproud.orgistic and also p-value.

Enter the table right into a Minitab worksheet as shown below:C1C2C3Likes TeaLikes Coffee-YesLikes Coffee-No12
Yes3025
No1035
Select stillproud.org > Tables > overcome Tabulation and also Chi-SquareSelect Summarized data in a two-way table indigenous the dropdownEnter the columns Likes Coffee-Yes and Likes Coffee-No in the Columns include the table boxFor the row labels go into Likes Tea (leave the obelisk labels blank)Select the Chi-Square button and check the boxes for Chi-square test and Expected cabinet counts.ClickOK and OKRows: Likes Tea Columns: Worksheet columnsNoYesAllYesNoAll
302555
2233
103545
1827
4060100
Cell contents:
Count
Expected count
Chi-Square TestChi-SquareDFP-ValuePearsonLikelihood Ratio
10.77410.001
11.13810.001

Since the assumption was met in action 1, we have the right to use the Pearson chi-square check stillproud.orgistic.

(Pearson;chi^2 = 10.774)


3. Determine a ns value associated with the test stillproud.orgistic.

(p = 0.001)


4. Decide between the null and alternate hypotheses.

Our p worth is less than the traditional 0.05 alpha level, so we reject the null hypothesis.


5. stillproud.orge a "real world" conclusion.

There is evidence of a relationship between between liking coffee and liking tea in the population.


A chi-square check of independence will provide you information concerning whether or no a relationship in between two categorical variables in the populace is likely. Together was the instance with the single sample and two sample theory tests the you learned earlier this semester, with a big sample dimension stillproud.orgistical power is high and the probability the rejecting the null hypothesis is high, also if the connection is reasonably weak. In addition to assessing stillproud.orgistical meaning by looking in ~ thepvalue, us can also examine practical significance by computing therelative risk.

In class 2 you learned that hazard is regularly used to explain the probability of an occasion occurring. Risk can likewise be provided to to compare the probabilities in two various groups. First, we"ll evaluation risk, then you"ll be presented to the principle of relative risk.

See more: Denotes A(N) ________ Directory That Is At The Top Of The Filing Structure Of A Computer.

Theriskof an outcome can it is in expressed as a fraction or as the percent that a group that experience the outcome.