Question

The name given to goodness of fit test was derived based on the hypothesis tested and how good the observed frequencies fit a given pattern. To make a goodness of fitness test, the sample size should be large enough so that the expected frequency for each category is at least 5.

There are four commonly used goodness of fit tests: The Chi-Square, Kolmogorov-Smirnov, Anderson-Darling, and Shipiro-Wilk.

Observed frequencies, denoted by O, are counts made from experimental data - whereby you observe the data happening and take measurements. Observed frequency is derived after the experiment has occurred.

The expected frequencies, denoted by E, on the other hand are counts calculated using probability theory resulting in the number of times a specific outcome is expected to occur (determined before the experiment). The expected frequency is calculated by E=np where "n' is the sample size and "p" is the probability that an element belongs to that category if the null hypothesis is true.  

The chi-square distribution is defined as having only one parameter called the degrees of freedom (df) - the number of independent pieces of information that goes into calculating estimates,

The shape of a chi-square distribution curve is skewed to the right for small degrees of freedom and becomes symmetric for large degrees of freedom, thus as the degrees of freedom increases the shape of the chi-square distribution changes.

When trying to remember the concept behind degrees of freedom - a good way to look at it is recalling the number of values that are free to vary in a data set. The text further explains that the entire chi-square distribution curve lies to the right of the vertical axis which assumes nonnegative values only.

Please in a minimum of 200 words:

What are some everyday examples of Chi-Squared that you can think of?

Mann, P. (2017). Introductory statistics (9th ed.). Wiley & Sons: Hoboken, NJ.

Answer 1

1.We’ll perform a Chi-square test of independence to determine whether there is a statistically significant association between shirt color and deaths. We need to use this test because these variables are both categorical variables. Shirt color can be only blue, gold, or red. Fatalities can be only dead or alive.

The color of the uniform represents each crew member’s work area. We will statistically assess whether there is a connection between uniform color and the fatality rate.

2.

We’ll perform a Chi-square test of independence to determine whether Education level and marital status are related for all people.

3.

We’ll perform a Chi-square test of independence to determine whether there is association between the students who score low marks and those
who can’t live without cell phone.

3.

We’ll perform a Chi-square test of independence to determine whether there is association between age group of youth and call time per day.