Question

Show how; Independent t-test , Coefficient of determination, Exploratory factor analysis, Chi-square test, Correlation coefficient, R-squared value, Analysis of covariance, Analysis of variance are applied in analysis of quantitative data ( explain in simple English please)

Answer 1

Independent t-test-

The independent t-test also known as the 2- sample t-test is a statistical test that determine whether there is a significant difference between the two means of the independent groups. We consider a hypothesis to carry out this test. To carry this test we make the following assumptions-

1. The data must follow a normal distribution

2. Homogenity of variance.

With the help of this test we make the conclusion such that if the p-value of the test is less than equal to the given significance level alpha we reject the null hypothesis.

Coefficient of Determination-

The coefficient of determination is a statistical measurement that shows how difference in one variable can be explained by the other variable i.e, it accesses the how strong the linear relationship between the two variables. The coefficient of determination is also known as the "goodness of fit". This measure ranges between 0 and 1 were a value of 1 indicates a perfect fit that is the model accurately makes future forecasts, while the value of 0 indicates that the model fails to do so.

Explanatory factor analysis-

Explanatory factor analysis is a technique that is used to reduce the data to a smaller set of variables and to explore the theoritical structure of it. It is used to identify the relationship between the variable and the respondant. This analysis can be performed by using two methods-

R-type factor analysis: When factors are calculated from the correlation matrix then it is called R-type factor analysis.

Q-type factor analysis: When the factors are calculated from the individual respondants then it is said to be Q-type factor analysis.

Chi-square test-

We cannot perform the chi-square test for analysis of quantitative data as it is done for qualitative or categorical data.

Chi-square test can be performed for qualitative data and has two types-

1. A chi-square goodness of fit test: It determines if a sample data matches its population of not.

2. A chi-square test for independence: It compares a relationship of two variables in a contingeny table.

Correlation Coefficient-

Correlation coefficients are used in statistics to measure how strong a relationship between two variables each. The most common type used is the Pearson's correlation coefficient. Its value ranges from -1 to 1, were 1 indicates a strong positive relationship, -1 indicates a strong negative relationship and 0 indicates no relationship.

R-squared value-

R-square is a statistical measure that represent the proportion between the variance of the dependent variable and the independent variable in a regression model. The formula for calculating the R-square is-

An R-squared of 100% means that all the movements of the dependent variable are completely explained by the movement of the independent variable.

Analysis of covariance-

Analysis of covariance or ANOCOVA allows to compare one variable in two or more groups taking into account the variability of other variables. ANOCOVA is a combination of one way or two analysis of variance with linear regression analysis. Here, we test for significance effect in the model. If the coefficient of linear regression is 0 then we proceed to test for the ANOVA part of the model otherwise we proceed with the usual ANOCOVA testing.

Analysis of variance-

Analysis of variance or ANOVA is a way to find out if the experimental result are significant. There are two types of ANOVA test-

1. One way: It has one independent variable with two levels.

2. Two way: It has two independent variables with multiple levels.

Here, we test for significance level in the model. If the null hypothesis is rejected we conclude the treatments are significantly different and opt for a paired comparison test to identify the significantly different pairs.