the range of chi-square assumes only values
Answers
Step-by-step explanation:
very small chi square test statistic means that your observed data fits your expected data extremely well. In other words, there is a relationship. A very large chi square test statistic means that the data does not fit very well. In other words, there isn't a relationship.
Answer:
The assumptions of the Chi-square include: The data in the cells should be frequencies, or counts of cases rather than percentages or some other transformation of the data. The levels (or categories) of the variables are mutually exclusive
Step-by-step explanation:
The Chi Square Statistic
Types of Data:
There are basically two types of random variables and they yield two types of data: numerical and categorical. A chi square (X2) statistic is used to investigate whether distributions of categorical variables differ from one another. Basically categorical variable yield data in the categories and numerical variables yield data in numerical form. Responses to such questions as "What is your major?" or Do you own a car?" are categorical because they yield data such as "biology" or "no." In contrast, responses to such questions as "How tall are you?" or "What is your G.P.A.?" are numerical. Numerical data can be either discrete or continuous. The table below may help you see the differences between these two variables.
Data Type Question Type Possible Responses
Categorical What is your sex? male or female
Numerical Disrete- How many cars do you own? two or three
Numerical Continuous - How tall are you? 72 inches
Notice that discrete data arise fom a counting process, while continuous data arise from a measuring process.
The Chi Square statistic compares the tallies or counts of categorical responses between two (or more) independent groups. (note: Chi square tests can only be used on actual numbers and not on percentages, proportions, means, etc.)
2 x 2 Contingency Table
There are several types of chi square tests depending on the way the data was collected and the hypothesis being tested. We'll begin with the simplest case: a 2 x 2 contingency table. If we set the 2 x 2 table to the general notation shown below in Table 1, using the letters a, b, c, and d to denote the contents of the cells, then we would have the following table:
Table 1. General notation for a 2 x 2 contingency table.
Variable 1
Variable 2
Data type 1
Data type 2
Totals
Category 1
a
b
a + b
Category 2
c
d
c + d
Total
a + c
b + d
a + b + c + d = N
For a 2 x 2 contingency table the Chi Square statistic is calculated by the formula:
Note: notice that the four components of the denominator are the four totals from the table columns and rows.
Suppose you conducted a drug trial on a group of animals and you hypothesized that the animals receiving the drug would show increased heart rates compared to those that did not receive the drug. You conduct the study and collect the following data:
Ho: The proportion of animals whose heart rate increased is independent of drug treatment.
Ha: The proportion of animals whose heart rate increased is associated with drug treatment.
