see attrachedWeek 14 Discussion Instructions Here we discuss the Chi-square goodness of fit and...

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see attrachedWeek 14 Discussion Instructions Here we discuss the Chi-square goodness of fit and Chi-square test of independence. This will be a detailed discussion worth 15 points so plan accordingly.  Please use the following Instructions to write your reply. Please follow the videos at  · Stats 3e Screencast 17.3 · Stats 3e Screencast 17.9 The Chapter 18 videos are optional.  For your reply, please: 1. Describe a scenario where you could use the Chi-square goodness of fit test OR the Chi-square test of independence. 2. Set up your test in SPSS and find out at what sample size the differences between groups become significant or at what counts per cell in the Chi-square test of independence the results become significant.   1. The point here is to get practice running one of the Chi-square methods and to see what relationship there is between sample size and the proportions you are comparing.  For example, if we go into a typical online classroom of 20 people and ask people whether they prefer one of three pizza toppings (cheese only, vegetables only, meat only), we might propose to expect an even distribution of scores, so 33% per category.   2. At 20 people, this is just over 6 people per group, so we might expect frequencies of Cheese (6 people), Vegetable (6 people), and Meat (8 people).  We would then compare our actual distribution of people's responses to these expectations using SPSS or an online Chi-square goodness of fit calculator to see if the counts per cell (frequencies or proportions) do or don't match the expected distribution of responses.  If our observed data is Cheese(n=3), Vegetable (n=3), and Meat (n=14), the Chi-square value is:  The Chi^2 value is 7.5. The p-value is .02352. The result is significant at p

Saravana · Accepted Answer

1. Describe a scenario where you could use the Chi-square goodness of fit test OR the Chi-square test of independence.
We would use Chi-square test whenever we want to check whether there is a relationship between two categorical (ordinal or nominal) variables. The test compares the observed frequency of the categorical variable to the frequency that would be expected by chance.
Following are some examples of scenarios requiring Chi- Square test:
Scenario1:
We categorized 100 participants into male, female, short and tall. Now we want to test whether being tall or short is influenced by sex. In this scenario we can use Chi-square test to the following hypothesis.
Categorical variables:
Height: Short or tall (Ordinal)
Sex: Male or Female (Nominal)
Alternate Hypothesis: Sex and Height (Short or tall) are related.
Null hypothesis: Sex and Height (short or tall) are not related
The observed distribution:
	Observed Distribution
	Male
	Female
	Row total
	Tall
	57
	24
	81
	Short
	14
	5
	19
	Column Total
	71
	29
	
So in this scenario we can use chi-square test whether being tall or short is influenced by gender.
Scenario2:
A researcher was interested to test whether cats could be trained to line dance. So researcher trained 200 cats by giving them either food or affection as reward for dance like behavior. After a week he counted number of cats that could line dance and number of cats that could not line dance. 
Categorical variable:  Dance (Yes or No) and Training ( food or affection)
The contingency table data:
	Training
	Food as reward
	Affection as reward
	Total
	Dance Yes
	28
	48
	76
	Dance No
	10
	114
	124
	Total
	38
	162
	200
We can now use Chi-square test to check whether nature of reward (food vs affection) influenced the probability of learning to dance in cats.
Scenario3:  We can test hypothesis like whether sex and opinion about gun permits or abortion are related to each other.
Our Hypothesis:
Alternate hypothesis: Sex and opinion about gun permits are related
Null hypothesis: Sex and opinion about gun permits are not related.
We can test the hypothesis in these scenarios using Chi-square tests.
Dataset:
We will use the Coin_data.sav data to understand the chi-square test of independence.
The dataset is a simulated experiment in which 25 male and 25 female toss a coin and the result of coin toss is noted as either Head or Tail. Each participant first tossed a biased coin that produced more Heads when tossed by males compared to females. The participant then tossed an unbiased coin whose output was not influence by gender of the participant. 
The data set contains three columns. 
Column1: “sex”: Nominal variable: Sex of the Participant
Column2: “biased”: Nominal variable: The head or tail results of coin toss from biased coin
Column3: “unbiased”: Nominal variable: The head or tail results of coin toss from unbiased coin
2. Set up your test in SPSS and find out at what sample size the differences between groups become significant or at what counts per cell in the Chi-square test of independence the results become significant.  
We want to test the whether the coin toss and gender of the participant is related in our dataset. We will test this hypothesis over the biased coin toss results in the column 3 of our dataset.
The hypothesis to test:
Alternate hypothesis:

Week 14 Discussion Instructions Here we discuss the Chi-square goodness of fit and Chi-square test of independence. This will be a detailed discussion worth 15 points so plan accordingly. Please use...

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