## Wednesday, May 28, 2014

### Overview of Correlation In Excel 2010 and Excel 2013

This is one of the following four articles on Correlations in Excel

Overview of Correlation In Excel 2010 and Excel 2013

Pearson Correlation in 3 Steps in Excel 2010 and Excel 2013

Pearson Correlation – Calculating r Critical and p Value of r in Excel

Spearman Correlation in 6 Steps in Excel 2010 and Excel 2013

# Overview of Correlation in Excel

Correlation analysis describes the strength of relationship between two variables. A positive correlation means that two variable usually move in the same direction, i.e., when one goes up, the other usually goes up as well. A negative correlation means that variables usually move in opposite directions, i.e., when one goes down, the other usually goes down. If changes in one variable can be closely estimated by changes in the other variable, the two variables have a high correlation.

If two variables have little or no correlation, there exists very little pattern between the movement of one variable and the movement of the other variable.

## Quick Indicator of a Correlation

The quickest way to see if a correlation exists between two variables is to plot them on a X-Y scatter-plot graph. The graph needs to indicate a monotonic relationship between the two variables in order to conclude that there might be a correlation. A monotonic relationship is one in which one variable generally moves in one direction (either always up or always down) when the other variable moves in a specific direction. In other words, when one variable goes up, the other variable usually always goes up as well or usually always goes down.\

Correlations can have values from -1 to +1. The closer the correlation value is to +1, the more positively correlated the two variables are. An X-Y scatterplot graph of two positively correlated variables looks like this: (Click On Image To See a Larger Version)

The closer the correlation value is to -1, the more negatively correlated the two variables are. An X-Y scatterplot graph of two negatively correlated variables looks like this: (Click On Image To See a Larger Version)

The closer the value of the correlation is to 0, the less correlated the two variables are. An X-Y scatterplot graph of two variables with very little correlation looks like this: (Click On Image To See a Larger Version)

## Causation

Using correlation to imply causation is probably the most frequently occurring incorrect use of statistics.

If data pairs X and Y are correlated, the following relationships are possible:

1) X causes Y

2) Y causes X

3) X and Y are consequences of a common cause, but do not cause each other;

4) There is no connection between X and Y; the correlation is coincidental.

Misinterpretation of correlation occurs when the correlation is interpreted to be the result of either point 1 or point 2 when in fact the underlying cause of the correlation was either point 3 or point 4. It is commonplace to find occurrences of correlation incorrectly being used to imply causation in advertising and political speeches.

It should be noted that while correlation does not mean causation, a causal relationship between can often not be ruled out. Correlation often indicates that a relationship between two variables might exist that warrants further investigation.

### Types of Data

Nominal data are categorical data whose order does not matter. Nominal data are merely name labels that are only used to differentiate but not to indicate any ordering of the data.

Ordinal data are categorical data whose order matter but there is no specific measurement of difference between values. A customer satisfaction scale or a Likert scale are examples of ordinal data.

Interval data are data whose difference between values is meaningful but the zero point is arbitrary. Fahrenheit and Celsius temperature scales are interval data.

Ratio data are data whose difference between values is meaningful and the zero point indicates that there is none of that variable. The absolute temperature scale is ratio data.

### Pearson Correlation vs. Spearman Correlation

The two types of correlations mostly commonly used are the Pearson Correlation and the Spearman Correlation.

The Pearson Correlation is generally used when the relationship between two variables appears to be linear, there are not too many outliers, and both variables are interval or ratio but not ordinal.

The Spearman Correlation is generally used the relationship between two variables appears to be nonlinear, there are many outliers, or at least one of the variables is ordinal.

An X-Y scatterplot graph of two variables whose correlation is linear looks like this: (Click On Image To See a Larger Version)

An X-Y scatterplot graph of two variables whose correlation is nonlinear looks like this: (Click On Image To See a Larger Version)

### Pearson Correlation’s Six Required Assumptions

1) The both variables are either interval or ratio data.

2) The Pearson Correlation is most accurate when the variables are approximately normally distribution. Normality is not an absolute requirement for applying the Pearson Correlation though. The text indicates that it is, but that is incorrect. I have uploaded an Excel workbook to the Doc Sharing folder that automatically checks normality by creates a Normal Probability Plot for input data.

3) The relationship is reasonably linear. This can be seen on an X-Y scatterplot.

4) Outliers are removed or kept to a minimum. Outliers can badly skew the Pearson correlation.

5) Each variable has approximately the same variance. In statistical terms, variables with the same variance are said to be homoscedastistic. Variance in data sets can be compared using the nonparametric tests Levene’s Test and the Brown-Forsythe Test. The F Test (available in Excel both as a function and as a Data Analysis tool) can be used to compare variance in data sets but is highly sensitive to non-normality of data.

6) There is a monotonic relationship between the two variables.

### Spearman Correlation’s Only Two Required Assumptions

1) The variables can be ratio, interval, or ordinal, but not nominal. Nominal variables are simply labels whose order doesn’t mean anything. The Spearman Correlation is nonparametric, i.e., the test’s outcome is not affected by the distributions of the data being compared.

2) There is a monotonic relationship between the two variables.

### Interesting History of Both Correlations

The inventors of the two correlations, Karl Pearson and Charles Spearman, were both professors in nearby universities in Europe at the beginning of the twentieth century. Each became the other’s arch-enemy as a result of their feud over the principles of correlation. Karl Pearson went on to become much more famous and is credited with creating the discipline of mathematical sciences. Further, the Pearson Correlation is more widely used in statistics than the Spearman Correlation, so it appears that Professor Pearson won the feud?

Excel Master Series Blog Directory

Statistical Topics and Articles In Each Topic

• Histograms in Excel
• Bar Chart in Excel
• Combinations & Permutations in Excel
• Normal Distribution in Excel
• t-Distribution in Excel
• Binomial Distribution in Excel
• z-Tests in Excel
• t-Tests in Excel
• Hypothesis Tests of Proportion in Excel
• Chi-Square Independence Tests in Excel
• Chi-Square Goodness-Of-Fit Tests in Excel
• F Tests in Excel
• Correlation in Excel
• Pearson Correlation in Excel
• Spearman Correlation in Excel
• Confidence Intervals in Excel
• Simple Linear Regression in Excel
• Multiple Linear Regression in Excel
• Logistic Regression in Excel
• Single-Factor ANOVA in Excel
• Two-Factor ANOVA With Replication in Excel
• Two-Factor ANOVA Without Replication in Excel
• Randomized Block Design ANOVA in Excel
• Repeated-Measures ANOVA in Excel
• ANCOVA in Excel
• Normality Testing in Excel
• Nonparametric Testing in Excel
• Post Hoc Testing in Excel
• Creating Interactive Graphs of Statistical Distributions in Excel
• Solving Problems With Other Distributions in Excel
• Optimization With Excel Solver
• Chi-Square Population Variance Test in Excel
• Analyzing Data With Pivot Tables
• SEO Functions in Excel
• Time Series Analysis in Excel
• VLOOKUP