Studied by 3 peopleDegrees of freedom
which depends on how chi-square is being used.
The population standard deviation is 𝜎=√2(df).
Population mean
μ = df
Random variable
X^2
Squared standard normal variables
χ2 = (Z1)^2 + (Z2)^2 + ... + (Zk)^2
The null and alternative hypotheses for GOF
may be written in sentences or may be stated as equations or inequalities.
Null hypothesis
The observed values of the data values and expected values are values you would expect to get.
Degrees of freedom GOF
Number of categories - 1
The goodness of fit is usually right-tailed
Large test statistic
Observed values and corresponding expected values are not close to each other.
Expected value rule
Needs to be above 5 to be able to use the test
Test of independence
Determines whether two factors are independent or not
The null hypothesis for independence
states that the factors are independent
The alternative hypothesis for independence
states that they are not independent (dependent).
Independence degrees of freedom
(number of columns -1)(number of rows - 1)
Expected value formula
(row total)(column total) / total number surveyed
Test for Homogeneity
used to draw a conclusion about whether two populations have the same distribution
Ho for Homogeneity
The distributions of the two populations are the same.
Ha for Homogeneity
The distributions of the two populations are not the same.
The test statistic for Homogeneity
Use a χ2 test statistic. It is computed in the same way as the test for independence.
Goodness-of-Fit
decides whether a population with an unknown distribution "fits" a known distribution.
Ho for GOF
The population fits the given distribution
Ha for GOF
The population does not fit the given distribution.
Independence
decides whether two variables are independent or dependent. There will be two qualitative variables and a contingency table will be constructed.
Ho for Independence
The two variables (factors) are independent.
Ha for Independence
The two variables (factors) are dependent.
Homogeneity
decides if two populations with unknown distributions have the same distribution as each other. There will be a single qualitative survey variable given to two different populations.
Ho of Homogeneity
The two populations follow the same distribution.
Ha of Homogeneity
The two populations have different distributions.
Degrees of freedom
which depends on how chi-square is being used.
The population standard deviation is 𝜎=√2(df).
Population mean
μ = df
Random variable
X^2
Squared standard normal variables
χ2 = (Z1)^2 + (Z2)^2 + ... + (Zk)^2
The null and alternative hypotheses for GOF
may be written in sentences or may be stated as equations or inequalities.
Null hypothesis
The observed values of the data values and expected values are values you would expect to get.
Degrees of freedom GOF
Number of categories - 1
The goodness of fit is usually right-tailed
Large test statistic
Observed values and corresponding expected values are not close to each other.
Expected value rule
Needs to be above 5 to be able to use the test
Test of independence
Determines whether two factors are independent or not
The null hypothesis for independence
states that the factors are independent
The alternative hypothesis for independence
states that they are not independent (dependent).
Independence degrees of freedom
(number of columns -1)(number of rows - 1)
Expected value formula
(row total)(column total) / total number surveyed
Test for Homogeneity
used to draw a conclusion about whether two populations have the same distribution
Ho for Homogeneity
The distributions of the two populations are the same.
Ha for Homogeneity
The distributions of the two populations are not the same.
The test statistic for Homogeneity
Use a χ2 test statistic. It is computed in the same way as the test for independence.
Goodness-of-Fit
decides whether a population with an unknown distribution "fits" a known distribution.
Ho for GOF
The population fits the given distribution
Ha for GOF
The population does not fit the given distribution.
Independence
decides whether two variables are independent or dependent. There will be two qualitative variables and a contingency table will be constructed.
Ho for Independence
The two variables (factors) are independent.
Ha for Independence
The two variables (factors) are dependent.
Homogeneity
decides if two populations with unknown distributions have the same distribution as each other. There will be a single qualitative survey variable given to two different populations.
Ho of Homogeneity
The two populations follow the same distribution.
Ha of Homogeneity
The two populations have different distributions.
Note
Flashcard