Correlation and Regression - ANOVA - DAY 5 - B.Ed - 8614 - AIOU
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The document discusses inferential statistics with a focus on regression analysis and ANOVA, outlining their purposes and methodologies. It explains regression's advantages in indicating relationships between variables and details the use of p-values in hypothesis testing. Additionally, it introduces SPSS as a statistical software tool and provides insights into ANOVA, its significance for comparing multiple groups, and key statistical concepts like variance and F-ratio.
Correlation and Regression - ANOVA - DAY 5 - B.Ed - 8614 - AIOU
- 2. Regression
- 3. Objectives of Regression Analysis
- 4. Why Do We Use Regression Analysis? There are multiple benefits of using regression analysis. These are as follows: ■ i) It indicates the significant relationships between dependent and the independent variables. ■ ii) It indicates the strength of impact of multiple independent variables on a dependent variable. ■ iii) It allows us to compare the effects of variables measured on different scales
- 5. Types of Regression ■ Commonly used types of regression are: ■ i) Linear Regression ■ It is the most commonly used types of regression. In this technique the dependent variable is continuous and the independent variable can be continuous or discrete and the nature of regression line is linear. ■ ii) Logistic Regression ■ Logistic regression is a statistical method for analyzing a data set in which there are one or more independent variables that determine an outcome. The outcome is measured with the dichotomous (binary) variable.
- 6. P-Value ■ The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of occurrence of a given event. A p-value is used in hypothesis testing to help researcher support or reject the null hypothesis. It is evidence against the null hypothesis. The smaller p-value is the stronger the evidence to reject the null hypothesis. If the p-value gets lower (i.e. closer to 0% and farther away from 100), a researcher is more inclined to reject the null hypothesis and accept the research hypothesis.
- 7. Conti. ■ A relatively simple way to interpret p-value is to think of them as representing how likely a result would occur by chance ■ For a calculated p-value of .01, we can say that the observed outcomes would be expected to occur by chance only 1 in 100 times in repeated tests on different samples of the population. Similarly a p-value of .05 would represent the expected outcome to occur by chance only 5 times out of 100 times in repeated tests and a p-value of .001 would represent the expected outcome to occur by chance only once if the same treatment is repeated for 1000 times on different samples of the population. In case of p-value .01, the researcher is 99% confident of getting similar results if same test is repeated for 100 times. Similarly in case of p-value .05, the researcher is 95% confident and in case of p-value .001, he is 999% confident of getting similar results if same test is repeated for 100 times and 1000 times respectively.
- 9. SPSS ■ SPSS Statistics is a software package used for interactive, or batched, statistical analysis. it was acquired by IBM in 2009. Current versions have the brand name: IBM SPSS Statistics. ■ SPSS is short for Statistical Package for the Social Sciences, and it's used by various kinds of researchers for complex statistical data analysis. The SPSS software package was created for the management and statistical analysis of social science data.
- 10. Why choose SPSS Statistics ■ Easier to use. Award-winning user interface offers ready access to deep analytical power. ■ Powerful. ... ■ Open source friendly. ... ■ Robust reporting and visualization. ... ■ Affordable. ... ■ No long-term commitment.
- 11. SPSS
- 12. Introduction ■ Analysis of Variance (ANOVA) is a statistical procedure used to test the degree to which two or more groups vary or differ in an experiment. This unit will give you an insight of ANOVA, its logic, one-way ANOVA, its assumptions, logic and procedure. F- distribution, interpretation of F-distribution and multiple procedures will also be discussed.
- 13. Introduction to Analysis of Variance (ANOVA) ■ The t-tests have one very serious limitation – they are restricted to tests of the significance of the difference between only two groups. There are many times when we like to see if there are significant differences among three, four, or even more groups. For example we may want to investigate which of three teaching methods is best for teaching ninth class algebra. In such case, we cannot use t-test because more than two groups are involved.
- 14. Cont…. ■ Analysis of Variance (ANOVA) is a hypothesis testing procedure that is used to evaluate mean differences between two or more treatments (or population). Like all other inferential procedures. ANOVA uses sample data to as a basis for drawing general conclusion about populations. Sometime, it may appear that ANOVA and t-test are two different ways of doing exactly same thing: testing for mean differences.
- 15. Cont…. ■ On the other hand ANOVA is used when we have two or more than two independent variables (treatment). Suppose we want to study the effects of three different models of teaching on the achievement of students. In this case we have three different samples to be treated using three different treatments. So ANOVA is the suitable technique to evaluate the difference.
- 16. Between-Treatment Variance ■ Variance simply means difference and to calculate the variance is a process of measuring how big the differences are for a set of numbers. The between- treatment variance is measuring how much difference exists between the treatment conditions. In addition to measuring differences between treatments, the overall goal of ANOVA is to evaluate the differences between treatments. Specifically, the purpose for the analysis is to distinguish between two alternative explanations.
- 17. Chance ■ The differences are simply due to chance. It there is no treatment effect, even then we can expect some difference between samples. The chance differences are unplanned and unpredictable differences that are not caused or explained by any action of the researcher. Researchers commonly identify two primary sources for chance differences.
- 18. Cont… ■ Individual Differences: Each participant of the study has its own individual characteristics. Although it is reasonable to expect that different subjects will produce different scores, it is impossible to predict exactly what the difference will be. ■ Experimental Error In any measurement there is a chance of some degree of error. Thus, if a researcher measures the same individuals twice under same conditions, there is greater possibility to obtain two different measurements. Often these differences are unplanned and unpredictable, so they are considered to be by chance.
- 19. Cont…. ■ when we calculate the between-treatment variance, we are measuring differences that could be either by treatment effect or could simply be due to chance. In order to demonstrate that the difference is really a treatment effect, we must establish that the differences between treatments are bigger than would be expected by chance alone. To accomplish this goal, we will determine how big the differences is when there is no treatment effect involved.
- 20. Within-Treatment Variance ■ Within each treatment condition, we have a set of individuals who are treated exactly the same and the researcher does not do anything that would cause these individual participants to have different scores.
- 21. The F-Distribution ■After analyzing the total variability into two basic components (between treatment and within treatment), the next step is to compare them. The comparison is made by computing a statistics called f-ratio. For independent measure ANOVA.
- 22. One Way ANOVA (Logic and Procedure) ■ The one way analysis of variance (ANOVA) is an extension of independent two-sample t-test. It is a statistical technique by which we can test if three or more means are equal. It tests if the value of a single variable differs significantly among three or more level of a factor.
- 23. Cont… ■ If one way ANOVA yields statistically significant result, we accept the alternate hypothesis (HA), which states that there are two group means that are statistically significantly different from each other. Here it should be kept in mind that one way ANOVA cannot tell which specific groups were statistically significantly different from each other. To determine which specific groups are different from each other.
- 24. Cont… ■ As there is only one independent variable or factor in one way ANOVA so it is also called single factor ANOVA. The independent variable has nominal levels or a few ordinal levels. Also, there is only one dependent variable and hypotheses are formulated about the means of the group on dependent variable. The dependent variable differentiates individuals on some quantitative dimension.
- 25. Procedure for Using ANOVA ■ In using ANOVA manually we need first to compute a total sum of squares (SS total) and then partition this value into two components: between treatments and within treatments.