What do correlations show

The Survey System's optional Statistics Module includes the most common type, called the Pearson or product-moment correlation. The module also includes a variation on this type called partial correlation. The latter is useful when you want to look at the relationship between two variables while removing the effect of one or two other variables.

Like all statistical techniques, correlation is only appropriate for certain kinds of data. Correlation works for quantifiable data in which numbers are meaningful, usually quantities of some sort. It cannot be used for purely categorical data, such as gender, brands purchased, or favorite color. Rating scales are a controversial middle case. The numbers in rating scales have meaning, but that meaning isn't very precise. They are not like quantities.

With a quantity such as dollars , the difference between 1 and 2 is exactly the same as between 2 and 3. With a rating scale, that isn't really the case. You can be sure that your respondents think a rating of 2 is between a rating of 1 and a rating of 3, but you cannot be sure they think it is exactly halfway between. This is especially true if you labeled the mid-points of your scale you cannot assume "good" is exactly half way between "excellent" and "fair".

This makes sense as a starting point, since we're usually looking for relationships and correlation is an easy way to get a quick handle on the data set we're working with. How do we define correlation? We can think of it in terms of a simple question: when X increases, what does Y tend to do? In general, if Y tends to increase along with X, there's a positive relationship.

If Y decreases as X increases, that's a negative relationship. Correlation is defined numerically by a correlation coefficient. This is a value that takes a range from -1 to 1. A coefficient of -1 is perfect negative linear correlation: a straight line trending downward. A correlation of 0 is no linear correlation at all. Here's a few examples of data sets that a correlation coefficient can accurately assess.

In finance, for example, correlation is used in several analyses including the calculation of portfolio standard deviation. Because it is so time-consuming, correlation is best calculated using software like Excel. Correlation combines statistical concepts, namely, variance and standard deviation. Variance is the dispersion of a variable around the mean, and standard deviation is the square root of variance.

There are several methods to calculate correlation in Excel. The simplest is to get two data sets side-by-side and use the built-in correlation formula:.

If you want to create a correlation matrix across a range of data sets, Excel has a Data Analysis plugin that is found on the Data tab, under Analyze. Select the table of returns. In this case, our columns are titled, so we want to check the box "Labels in first row," so Excel knows to treat these as titles. Then you can choose to output on the same sheet or on a new sheet.

Once you hit enter, the data is automatically created. You can add some text and conditional formatting to clean up the result. The linear correlation coefficient is a number calculated from given data that measures the strength of the linear relationship between two variables, x and y.

Correlation combines several important and related statistical concepts, namely, variance and standard deviation. The formula is:. The computing is too long to do manually, and sofware, such as Excel, or a statistics program, are tools used to calculate the coefficient. As variable x increases, variable y increases.

As variable x decreases, variable y decreases. A correlation coefficient of -1 indicates a perfect negative correlation. As variable x increases, variable z decreases. As variable x decreases, variable z increases. A graphing calculator is required to calculate the correlation coefficient. The following instructions are provided by Statology. Step 1: Turn on Diagnostics. You will only need to do this step once on your calculator.

After that, you can always start at step 2 below. This is important to repeat: You never have to do this again unless you reset your calculator. Step 2: Enter Data. Step 3: Calculate! Finally, select 4:LinReg and press enter. Now you can simply read off the correlation coefficient right from the screen its r. This is also the same place on the calculator where you will find the linear regression equation and the coefficient of determination.

The linear correlation coefficient can be helpful in determining the relationship between an investment and the overall market or other securities. It is often used to predict stock market returns. This statistical measurement is useful in many ways, particularly in the finance industry. For example, it can be helpful in determining how well a mutual fund is behaving compared to its benchmark index, or it can be used to determine how a mutual fund behaves in relation to another fund or asset class.

By adding a low, or negatively correlated, mutual fund to an existing portfolio, diversification benefits are gained. Fundamental Analysis. Financial Analysis. It's important to note that this does not mean that there is not a relationship at all; it simply means that there is not a linear relationship. Correlations can be confusing, and many people equate positive with strong and negative with weak.

A relationship between two variables can be negative, but that doesn't mean that the relationship isn't strong. A weak positive correlation would indicate that while both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, would indicate a strong connection between the two variables, but that one goes up whenever the other one goes down.

Of course, correlation does not equal causation. Just because two variables have a relationship does not mean that changes in one variable cause changes in the other. Correlations tell us that there is a relationship between variables, but this does not necessarily mean that one variable causes the other to change.

An oft-cited example is the correlation between ice cream consumption and homicide rates. Studies have found a correlation between increased ice cream sales and spikes in homicides.

However, eating ice cream does not cause you to commit murder. Instead, there is a third variable: heat. Both variables increase during summertime. An illusory correlation is the perception of a relationship between two variables when only a minor relationship—or none at all—actually exists. An illusory correlation does not always mean inferring causation; it can also mean inferring a relationship between two variables when one does not exist.

For example, people sometimes assume that because two events occurred together at one point in the past, that one event must be the cause of the other. These illusory correlations can occur both in scientific investigations and in real-world situations.

Stereotypes are a good example of illusory correlations. Research has shown that people tend to assume that certain groups and traits occur together and frequently overestimate the strength of the association between the two variables.