What us the difference between chi-square, z-test, and t-test
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Answers ( 6 )
chi square :- used as a test of independence of two categorical variables
z test- A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size >30.
t test -hypothesis testing used for variance is unknown and sample size<30 The t test is one type of inferential statistics. It is used to determine whether there is a significant difference between the means of two groups
A t-test tests the null hypothesis of two means.
It is used when varaince is unknown and sample size is less than 30
Z-test is similar to t-test. It is used when the sample size is greater than 30
Chi square test is used to examine the difference between two categorical variables in the same population.
Pearson’s chi-square test : used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.
Z-test is a type of hypothesis test. Hypothesis testing is just a way for you to figure out if results from a test are valid or repeatable.
T-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. Unlike Z-test it is used when sample size is less than 30
Chi -Square is used to check how independent two categorical variables are.
t-test is used when sample size is less than 30 and it is used to test mean of two samples
z-test is similar to t-test the difference is sample size is greater than 30
t-test:
1) A t-test tests a null hypothesis about two means; most often, it tests the hypothesis that two means are equal, or that the difference between them is zero. For example, we could test whether boys and girls in fourth grade have the same average height.
2) A t-test requires two variables; one must be categorical and have exactly two levels, and the other must be quantitative and be estimable by a mean. For example, the two groups could be Republicans and Democrats, and the quantitative variable could be age
3) t-tests are most helpful with a smaller sample size (n 30
chi-square test:
1) A chi-square test tests a null hypothesis about the relationship between two variables. For example, you could test the hypothesis that men and women are equally likely to vote “Democratic,” “Republican,” “Other” or “not at all”
2) A chi-square test requires categorical variables, usually only two, but each may have any number of levels
Z-test:
In a z-test, the sample is assumed to be normally distributed. A z-score is calculated with population parameters such as “population mean” and “population standard deviation” and is used to validate a hypothesis that the sample drawn belongs to the same population. Preferred when n > 30.
Null: Sample mean is same as the population mean
Alternate: Sample mean is not same as the population mean
The statistics used for this hypothesis testing is called z-statistic, the score for which is calculated as
z = (x — μ) / (σ / √n), where
x= sample mean
μ = population mean
σ / √n = population standard deviation
If the test statistic is lower than the critical value, accept the hypothesis or else reject the hypothesis.
T-test:
A t-test is used to compare the mean of two given samples. Like a z-test, a t-test also assumes a normal distribution of the sample. A t-test is used when the population parameters (mean and standard deviation) are not known. Preferred when n < 30.
There are three versions of t-test
1. Independent samples t-test which compares mean for two groups
2. Paired sample t-test which compares means from the same group at different times
3. One sample t-test which tests the mean of a single group against a known mean.
The statistic for this hypothesis testing is called t-statistic, the score for which is calculated as
t = (x1 — x2) / (σ / √n1 + σ / √n2), where
x1 = mean of sample 1
x2 = mean of sample 2
n1 = size of sample 1
n2 = size of sample 2
Chi-Square Test:
Chi-square test is used to compare categorical variables. There are two type of chi-square test
1. Goodness of fit test, which determines if a sample matches the population.
2. A chi-square fit test for two independent variables is used to compare two variables in a contingency table to check if the data fits.
a. A small chi-square value means that data fits
b. A high chi-square value means that data doesn’t fit.
The hypothesis being tested for chi-square is
Null: Variable A and Variable B are independent
Alternate: Variable A and Variable B are not independent.
The statistic used to measure significance, in this case, is called chi-square statistic. The formula used for calculating the statistic is
Χ2 = Σ [ (Or,c — Er,c)2 / Er,c ] where
Or,c = observed frequency count at level r of Variable A and level c of Variable B
Er,c = expected frequency count at level r of Variable A and level c of Variable B