Question

Provide an example of where you could use correlation in real life. Explain why a t-test is necessary before you accept this correlation as being real in the population.

"Please give extreme step by step actions on how to explain this, so that I can understand to explain to class".

Answer 1

Before to give any real life example it's necessary to know the exact meaning of "Correlation". Many proponents have defined the correlation in different way but each have the same meaning i.e. 'If the change in one variable affects a change in the other variable, the variables are said to be correlated'. It has two type.

Positive Correlation: If the two variables deviate in the same direction, i.e., if the increase (or decrease) in one results in a corresponding increase (or decrease) in the other, correlation is said to be direct or positive.

Negative Correlation: If the two variables constantly deviate in the opposite direction, i.e., if the increase (or decrease) in one results in a corresponding decrease (or increase) in the other, correlation is said to be diverse or negative.

There are many real life based example of correlation. Few of them are-

As the temperature goes up, ice cream sales also go up. For more details, you can collect one month (say) of data. Like how much ice cream, a seller sales in a day. Now accordingly collect the data of one month and then analyze it. You will be able to see that when the temperature goes up, how the sales of ice cream also go up. From here you can also find the monthly average about the dependency of people on ice cream, when temperature goes up.

t-test in Correlation

Two sample comparison of means testing of two sample t test with equal variances can be turned into a correlation problem by combining the two samples into one (random variable x) and setting the random variable y (the dichotomous variable) to 0 for elements in one sample and to 1 for elements in the other sample. It turns out that the two-sample analysis using t-test equivalent to the analysis of the correlation coefficient using the t-test.

Hence we can say that t-test is necessary before to accept the correlation as being real in the population.