Question

• What does the Pearson correlation tell us about the variables (3 things)?

• What type of data is utilized in order to perform a Pearson correlation?

• What is the Chi-Square Goodness of fit Test?

• What are the two frequencies measured during the Chi Square Goodness of Fit test and what is the difference between the two?

• What type of data is utilized in order to perform a Chi Square Goodness of Fit test?

• How do you determine the degrees of freedom for the one-way ANOVA, Pearson correlation, and the Chi Square Goodness of Fit test?

Answer 1

What does the Pearson correlation tell us about the variables?

The Pearson product-moment correlation coefficient (or Pearson correlation coefficient, for short) is a measure of the strength of a linear association between two variables and is denoted by r. Basically, a Pearson product-moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit.

The Pearson correlation coefficient, r, can take a range of values from +1 to -1. A value of 0 indicates that there is no association between the two variables. A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable. A value less than 0 indicates a negative association; that is, as the value of one variable increases, the value of the other variable decreases.

What type of data is utilized in order to perform a Pearson correlation?

Correlation is a technique for investigating the relationship between two quantitative, continuous variables, for example, age and blood pressure. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables.

The first step in studying the relationship between two continuous variables is to draw a scatter plot of the variables to check for linearity. The correlation coefficient should not be calculated if the relationship is not linear. For correlation only purposes, it does not really matter on which axis the variables are plotted. However, conventionally, the independent (or explanatory) variable is plotted on the x-axis (horizontally) and the dependent (or response) variable is plotted on the y-axis (vertically).

The nearer the scatter of points is to a straight line, the higher the strength of association between the variables.

What is the Chi-Square Goodness of fit Test?

In the case of attributes we use this test

Hypothesis to be tested:

H0: The given variables are independent.

H1: The given variables are dependent.

• Compute the value of Chi-Square goodness of fit test using the following formula:

Where, = Chi-Square goodness of fit test O= observed value E= expected value

• Degree of freedom: In Chi-Square goodness of fit test, the degree of freedom depends on the distribution of the sample. The following table shows the distribution and an associated degree of freedom: n-1.

What are the two frequencies measured during the Chi Square Goodness of Fit test and what is the difference between the two?

This lesson explains how to conduct a chi-square goodness of fit test. The test is applied when you have one categorical variable from a single population. It is used to determine whether sample data are consistent with a hypothesized distribution.

For example, suppose a company printed baseball cards. It claimed that 30% of its cards were rookies; 60% were veterans but not All-Stars; and 10% were veteran All-Stars. We could gather a random sample of baseball cards and use a chi-square goodness of fit test to see whether our sample distribution differed significantly from the distribution claimed by the company.

What type of data is utilized in order to perform a Chi Square Goodness of Fit test?

Chi-Square goodness of fit test is a non-parametric test that is used to find out how the observed value of a given phenomena is significantly different from the expected value. In Chi-Square goodness of fit test, the term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. Chi-Square goodness of fit test determines how well theoretical distribution (such as normal, binomial, or Poisson) fits the empirical distribution. In Chi-Square goodness of fit test, sample data is divided into intervals. Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval.

How do you determine the degrees of freedom for the one-way ANOVA, Pearson correlation, and the Chi Square Goodness of Fit test?

When we wish to know whether the means of two groups (one independent variable (e.g., gender) with two levels (e.g., males and females) differ, a t test is appropriate. In order to calculate a t test, we need to know the mean, standard deviation, and number of subjects in each of the two groups.It is the number of subjects minus the number of groups (always 2 groups with a t-test).

If the independent variable (e.g., political party affiliation) has more than two levels (e.g., Democrats, Republicans, and Independents) to compare and we wish to know if they differ on a dependent variable (e.g., attitude about a tax cut), we need to do an ANOVA (ANalysis Of VAriance). In other words, if we have one independent variable (with three or more groups/levels) and one dependent variable, we do a one-way ANOVA.

Chi-Square

We might count the incidents of something and compare what our actual data showed with what we would expect.