Sample Homework Question no.7

Course: Marketing - Statistics
Level: Undergraduate

Question:

Explain when it is appropriate to use averages when computing correlations. Explain what statisticians should be aware of when doing this.

Additional notes: 2 paragraphs with examples please

Answer:

The Pearson product moment correlation uses the averages of the variables in the formula. So care should be taken when choosing the method of correlation to be used. For example: considered the variables to be the rank obtained by the students in English and Mathematics. When we try to find the correlation between the variables we should be aware that the values of the discussed variable are nothing but ranks. If we wanted to use the product moment correlation for the variables, we would average the ranks and use the averages to find the coefficient of correlation. But there is no real meaning if you say that the average of the student rank is 3.5. So spearman rank correlation is better to use in this situation. One should be aware of the level of measurement of the variables, whether the variables are ordinal or interval. In conclusion, whenever both the variables are intervals, we can use the Pearson’s product moment correlation and whenever one of the variables is ordinal, the spearman rank correlation is suggested.

1. Random Variables - A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon.

2. Correlation Coefficient - a measure of the correlation of two variables X and Y measured on the same object or organism, that is, a measure of the tendency of the variables to increase or decrease together.

3. Interval Scale -You are also allowed to quantify the difference between two interval scale values but there is no natural zero. For example, temperature scales are interval data with 25C warmer than 20C and a 5C difference has some physical meaning. Note that 0C is arbitrary, so that it does not make sense to say that 20C is twice as hot as 10C.

4. Ordinal Scale - You are also allowed to examine if an ordinal scale datum is less than or greater than another value. Hence, you can 'rank' ordinal data, but you cannot 'quantify' differences between two ordinal values. For example, political party is an ordinal datum with the NDP to left of Conservative Party, but you can't quantify the difference. Another example, are preference scores, e.g. ratings of eating establishments where 10=good, 1=poor, but the difference between an establishment with a 10 ranking and an 8 ranking can't be quantified.

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