Parametric Test

This ppt is related to parametric test and it's application.

1. NAME – AMRITA KUMARI AFFILIATION – BANARAS HINDU UNIVERSITY A p p lication n o . - 8 f f f 9 9 e 6 7 c 1 1 e 9 8 1 3 3 9 e 3 a 9 5 7 6 9 a c

2. PARAMETRIC TESTS Parametric function were mentioned by R.Fisher . It’s a statistical test in which specific assumptions are made about the population distribution from which the sample is drawn. ASSUMPTIONS : The population data is normally distributed. The observations must be independent. The population must have same variance. The samples drawn from population must follow homogenity principle . The data should be on ratio or interval scale.

3. WHEN & WHY WE DO PARAMETRIC TEST? It can perform well with skewed and non normal distributions. It can also be done when the spread of each group is different. It has more statistical power.

4. TYPES OF PARAMETRIC TEST Z-test ANOVA One-way ANOVA Two-way ANOVA t - t e s t O n e - s a m p l e t - t e s t T w o s a m p l e T w o s a m p le t - t e s t

5. t-test

6. t-test It’s a method of testing hypothesis about the mean of small sample drawn from a normally distributed population when SD(standard deviation) for the sample is unknown. ASSUMPTIONS Observations in the study are independent of each other. Homogeneity of variance : distribution of scores around mean are of 2 or more samples are equal

7. sample is drawn from a normally distributed population. DVs are on interval or ratio scale. TYPES OF t-test

8. ONE SAMPLE t- test It’s used to measure whether a sample value significantly differs from a hypothesized value. For eg: a research scholar might hypothesize that on an average it takes 3 minutes for people to drink a standard cup of coffee. He conducts an experiment & measures how long it takes his subjects to drink a standard cup of coffee. The one sample t-test measures whether the mean amount of time it took the experimental group to complete the task varies significantly from the hypothesized 3 min value.

9. Equation for one-sample t-test

10. DEPENDENT t-test It compares the means of two related samples to check whether there is a significant difference between their means. It is an example of within subjects or repeated measures statistical tests.

11. HYPOTHESIS  

12. STEPS TO CALCULATE

13. After getting the t value calculate the degree of freedom. Now we look at the critical value from the table for the significance level of 0.05 or 0.01 for the degree of freedom we got. If our t value obtained is greater than the critical value, the null hypothesis is rejected and the alternate hypothesis is accepted. Hence, this is how correlated t test is calculated.

14. Independent t-test is used when means of two different samples are compared. The two independent samples are randomly selected and are completely independent of each other. The distribution of dependent variable is normal in the populations from which samples are drawn and the variances in the population are roughly equal. Data are measured at least at interval level. TWO SAMPLE :INDEPENDENT t-test

15. We test the null hypothesis that the two population means are same against an appropriate one-tailed or two-tailed alternative hypothesis. µ1 = µ2 Where µ1 = Mean of population 1 and µ2 = Mean of population 2 Since null hypothesis assumes that means of both populations are same, then µ1 - µ2 = 0

16. STEPS TO CALCULATE

17. ADVANTAGES AND DISADVANTAGES OF PARAMETRIC STATISTICS

18. Does not require convertable data- biggest advantage. The long calculations provide accuracy and precision to the results. In this specific assumption are made about the population. Based on distribution. There is complete information about the population. Can perform quite well when they have been spread over and each group happens to be different. It has high statistical power as compared to other tests. Therefore we will be able to find an effect that is significant when one will exist truly. ADVANTAGES

19. DISADVANTAGES Influence of sample size- parametric tests are not valid when it comes to small sample (if < n=10). You have missing values as well as outliers, you just cannot randomly remove. Susceptibility to violation of assumptions Scope of application Speed of application Ease of application Simplicity of deviation- high level of maths calculations. Parametric test is used for only interval data and ratio data.

20. Acknowledgement SWAYAM o n l i ne c ourse - A c a d e mic w r i t ing

21. R e f e rence s W e k i pedia . Win er, , B . J . , Brown , D . R . & Michel s , K . M . ( 1 9 9 1 ) Statis t ical principles i n e x p e r i m ental d e sign . N Y : M c G r a w H i l l .