Parametric Statistical tests

In Hypothesis testing parametric test is very important. in this ppt you can understand all types of parametric test with assumptions which covers Types of parametric, Z-test, T-test, ANOVA, F-test, Chi-Square test, Meaning of parametric, Fisher, one-sample z-test, Two-sample z-test, Analysis of Variance, two-way ANOVA.
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1. Submitted by, Pooja . G. G.F.G.C.W Holenarsipura P.G Studies . PARAMETRIC TEST

2. CONTENT Meaning of parametric. Types of parametric. 1. Z-test. 2. T-test. 3. ANOVA. 4. F-test. 5. Chi-Square test.

3. Meaning of parametric Parametric statistic is a branch of statistic, which assumes that sample data comes from a population that follows a probability or normal distribution. When the assumption are correct, parametric methods will produce more accurate and precise estimates.

4. Types of parametric The types of parametric are, Z- test. T-test. ANOVA. F-test. Chi-Square test.

5. 1. Z-test. A Z-test is given by Fisher. A Z-test is a type of hypothesis test or statistical test. It is used for testing the mean of a population versus a standard or comparing the means of two population with large sample (n>30). When we can run a Z-test Your sample size is greater than 30. Data point should be independent from each other. Your data should be randomly selected from a population, where each item has an equal chance of being selected.

6. Continue…. Data should follow normal distribution. The standard deviation of the populations is known. There are two ways to calculate z-test a. one-sample z-test. b. two-sample z-test.

7. a. one-sample z-test One-sample z-test we are comparing the mean, calculated on a single of score (one sample) with known standard deviation. Ex. The manager of a candy manufacture wants to know whether the mean weight of batch of candy boxes is equal to the target value of 10 pounds from historical data .

8. b. Two-sample z-test When testing for the differences between two groups can imagine two separate situation. Comparing the proportion of two population. In two sample z-test both independent populations. Ex: 1. Comparing the average engineering salaries of men versus women . 2. Comparing the fraction defectives from two production line .

9. 2. T- tset . It is derived by W.S Gosset in 1908. It is also called student t-test. A t-test statistical significance indicates whether or not the difference between two groups. Assumption: Samples must be random and independent. When samples are small. n<30 Standard deviation is not known. Normal distribution.

10. Continue… There are two ways to calculate T-test such as, Unpaired t-test.(independent) Paired t-test. a. Unpaired t-test: If there is no link between the data then use the unpaired t-test. When two separate set of independent sample are obtain one from each of the two population being compared. Ex:1. Compare the height of girls and boys. 2. Compare the 2 stress reduction intervention. When one group practiced mindfulness meditation, while other learned yoga.

11. b. Paired t-test. Paired t-test consists of a sample of matched pairs of similar units or one group of units that has been tested twice (a” repeated measures” t-test). If there is some link between the data then use the paired t-test.(e.g. Before and after) Ex: 1. where subject are tested prior to a treatment say for high blood pressure, and the same subject are tested again after treatment with a blood pressure lowering medication. 2. Test on person or any group before and after training.

12. 3. ANOVA ( Analysis of Variance) It is developed by Fisher in 1920. ANOVA is a collection of statistical model used to analyze the differences between groups. Compare multiple groups at one time. It is advanced technique for the experimental treatment of testing differences all of the mean which is not possible in case of t-test. Assumptions: All population have same standard deviation. Individuals in population are selected randomly. Independent samples. The population must be normal distribution .

13. There are two ways to calculate ANOVA such as. one-way ANOVA. Two-way ANOVA. a. one-way ANOVA: One-way anova compare three or more unmatched groups when data are categorized in one way. Ex: You might be studying the effect of tea on weight loss, from three groups, green tea, black tea, no tea.

14. b. two-way ANOVA Two way anova technique is used when the data are classified on the basis of two factors. And two way anova analyzed a 2 independent variable and 1 dependent variable. Ex: The agricultural output may be classified on the basis of different verities of seeds. and also on the basis of different verities of fertilizer used.

15. 4. F-test It is derived by Fisher in 1924. The F-test is designed to test if two population variance are equal. There are two independent degrees of freedom, one for numerator another one is denominator. Numerator: the numerator degrees of freedom will be the degree of freedom for whichever sample has the larger variance. s ¹ Denominator: the denominator degrees of freedom will be the degree of freedom for whichever sample has the small variance. s ² Assumption: Samples are drawn at random. There is no measurement error. F-values are all non negative.

16. Ex: Two source of raw materials are under consideration by a company. Both source seem to have similar characteristics but the company is not sure about their respective uniformity. A sample of 10 lots source X yields a variance of 225 and a sample of 11 lots from source Y yield a variance of 200. is it likely that the variance of source X is significantly greater than the variance of source Y at ɑ=0.01? Formula: F= S²₁(numerator) S²₂(denominator)

17. 5. Chi-Square test It is drawn by Karl Pearson. Chi square test is a statistical test used as a parametric for testing for comparing variance . It is denoted as “ x²”. Formula: