Workshop on Data Analysis and Result Interpretation in Social Science Research Day 2- parametric test
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This document discusses parametric and nonparametric statistical tests. Parametric tests like the t-test and ANOVA assume a normal distribution of data and compare population means. Nonparametric tests do not assume a normal distribution and can be used when sample sizes are small or distributions are unknown. Specific parametric tests covered include the t-test for comparing two groups, one-way ANOVA for comparing three or more groups on one factor, and two-way ANOVA for examining two factors. Examples of how and when to use these various tests are provided.
Workshop on Data Analysis and Result Interpretation in Social Science Research Day 2- parametric test
- 1. Parametric Test t- Test F-Test Dr. Jai Singh
- 2. Parametric/ Non Parametric • A parametric statistical test makes an assumption about the population parameters and the distributions that the data came from. • Parametric tests assume a normal distribution of values, or a “bell-shaped curve.” • These types of test includes Student’s T tests and ANOVA tests, which assume data is from a normal distribution. • The opposite is a nonparametric test, which doesn’t assume anything about the population parameters. • Nonparametric tests include chi-square, Fisher’s exact test and the Mann-Whitney test.
- 3. Nonparametric tests • Nonparametric tests are used in cases where parametric tests are not appropriate. • some way of ranking the measurements and testing for oddness of the distribution.
- 4. When to use nonparametric tests • distribution is not normal (the distribution is skewed), • the distribution is not known, • or the sample size is too small (<30) to assume a normal distribution. • extreme values or values -“out of range,”
- 5. Various Parametric tests • The most widely used tests are the t-test (paired or unpaired), • ANOVA (one-way, two-way, three-way), • linear regression and • Pearson rank correlation.
- 6. t- Test • A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups. • Essentially, a t-test allows us to compare the average values of the two data sets and determine if they came from the same population. • It is mostly used when the data sets would follow a normal distribution and may have unknown variances. • Ex. difference in mean score in Mathematics achievement of boys and girls, rural and urban area, mean score of students taught by traditional method and online learning etc.
- 7. Use of t-Test Students would not expect them to have exactly the same mean and standard deviation Class-A Class-B Control Group Drug Prescribed Group Same Population ?
- 8. Formula for t -Test t= M1-M2 √ δ1 2/ N1+ δ2 2/ N2 Where M1= Mean of First group M2 = Mean of Second group δ1 = SD of first group δ2 = SD of second group N1 = Number of cases in first group N2 = Number of cases in second group
- 9. Analysis of Variance (ANOVA) • F-Test or Analysis of Variance (ANOVA) - An inferential statistics used to determine the significant difference of three or more variables or multivariate collected from experimental research. • This is usually applied in single-group design and complete randomized design (CRD).
- 10. One-Way ANOVA • One way Analysis of Variance (ANOVA) is a hypothesis test in which only one categorical variable or single factor is considered. • It is a technique which enables us to make a comparison of means of three or more samples with the help of F-distribution. • It is used to find out the difference among its different categories having several possible values. • The null hypothesis (H0) is the equality in all population means, while alternative hypothesis (H1) will be the difference in at least one mean.
- 11. Two-Way ANOVA • - is a hypothesis test wherein the classification of data is based on two factors. - For instance, the two bases of classification for the sales made by the firm is first on the basis of sales by the different salesman and second by sales in the various regions. • It is a statistical technique used by the researcher to compare several levels (condition) of the two independent variables involving multiple observations at each level. • Two-way ANOVA examines the effect of the two factors on the continuous dependent variable. • It also studies the inter-relationship between independent variables influencing the values of the dependent variable, if any.
- 12. Key Differences Between One-Way and Two-Way ANOVA • The differences between one- way and two-way ANOVA can be drawn clearly on the following grounds: • A hypothesis test that enables us to test the equality of three or more means simultaneously using variance is called One way ANOVA. • A statistical technique in which the interrelationship between factors, influencing variable can be studied for effective decision making, is called Two-way ANOVA. • There is only one factor or independent variable in one way ANOVA whereas in the case of two-way ANOVA there are two independent variables. • One-way ANOVA compares three or more levels (conditions) of one factor. On the other hand, two-way ANOVA compares the effect of multiple levels of two factors.
- 13. Example- • Supposed the researcher wishes to determine the effectiveness of teaching science using traditional method (Method 1), blended learning (Method 2), online learning (Method 3) to Graduate science students. • The specific research problem – “Is there a significant difference on the Effectiveness of Teaching Science using Method 1, Method 2, and Method 3 to Graduate science Students? ” • Independent Variables- Method of Teaching I Method of Teaching II Method of Teaching III • Dependent Variables - Mean Grade in: Semester I to Semester-6th
- 14. Null Hypothesis for Problem • Null Hypothesis: There is no significant difference on the mean grade of students taught by traditional method, blended method and online method.
- 15. Example for One Way Anova Research Hypothesis- • Is there difference in high school students’ level of satisfaction with school based on there family socio-economic status? Null Hypothesis- • There is no significant difference in high school students’ level of satisfaction with the school based on their family’s socio-economic status.