How do I interpret data in SPSS for Pearson's r and scatterplots?

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## Correlations Box

Take a look at the first box in your output file called Correlations. You will see your variable names in two rows. In this example, you can see the variable name ‘water’ in the first row and the variable name ‘skin’ in the second row. You will also see your two variable names in two columns. See the variable names ‘water’ and ‘skin’ in the columns on the right? You will see four boxes on the right hand side. These boxes will all contain numbers that represent variable crossings. For example, the top box on the right represents the crossing between the ‘water’ variable and the ‘skin’ variable. The bottom box on the left also happens to represent this crossing. These are the two boxes that we are interested in. They will have the same information so we really only need to read from one. In these boxes, you will see a value for Pearson’s r, a Sig. (2-tailed) value and a number (N) value. ## Pearson’s r

You can find the Pearson’s r statistic in the top of each box. The Pearson’s r for the correlation between the water and skin variables in our example is 0.985. ## When Pearson’s r is close to 1…

This means that there is a strong relationship between your two variables. This means that changes in one variable are strongly correlated with changes in the second variable. In our example, Pearson’s r is 0.985. This number is very close to 1. For this reason, we can conclude that there is a strong relationship between our water and skin variables. However, we cannot make any other conclusions about this relationship, based on this number.

## When Pearson’s r is close to 0…

This means that there is a weak relationship between your two variables. This means that changes in one variable are not correlated with changes in the second variable. If our Pearson’s r were 0.01, we could conclude that our variables were not strongly correlated.

## When Pearson’s r is positive (+)…

This means that as one variable increases in value, the second variable also increase in value. Similarly, as one variable decreases in value, the second variable also decreases in value. This is called a positive correlation. In our example, our Pearson’s r value of 0.985 was positive. We know this value is positive because SPSS did not put a negative sign in front of it. So, positive is the default. Since our example Pearson’s r is positive, we can conclude that when the amount of water increases (our first variable), the participant skin elasticity rating (our second variable) also increases.

## When Pearson’s r is negative (-)…

This means that as one variable increases in value, the second variable decreases in value. This is called a negative correlation. In our example, our Pearson’s r value of 0.985 was positive. But what if SPSS generated a Pearson’s r value of -0.985? If SPSS generated a negative Pearson’s r value, we could conclude that when the amount of water increases (our first variable), the participant skin elasticity rating (our second variable) decreases.

## Sig (2-Tailed) value

You can find this value in the Correlations box. This value will tell you if there is a statistically significant correlation between your two variables. In our example, our Sig. (2-tailed) value is 0.002. ## If the Sig (2-Tailed) value is greater than 05…

You can conclude that there is no statistically significant correlation between your two variables. That means, increases or decreases in one variable do not significantly relate to increases or decreases in your second variable.

If the Sig (2-Tailed) value is less than or equal to .05…

You can conclude that there is a statistically significant correlations between your two variables. That means, increases or decreases in one variable do significantly relate to increases or decreases in your second variable.

## Our Example

The Sig. (2-Tailed) value in our example is 0.002. This value is less than .05. Because of this, we can conclude that there is a statistically significant correlation between amount of water consumed in glasses and participant rating of skin elasticity.

## Warning about the Sig (2-Tailed) value

When you are computing Pearson’s r, significance is a messy topic. When you have small samples, for example only a few participants, moderate correlations may misleadingly not reach significance. When you have large samples, for example many participants, small correlations may misleadingly turn out to be significant. Some researchers think  that significance should be reported but perhaps should receive less focus when it comes to Pearson’s r.

## So what about the scatterplot?

You can find your scatterplot in your output file. It will look something like the graph below. You will see a bunch of dots. Your scatterplot can tell you about the relationship between variables, just like Pearson’s r. With it, you can determine the strength and direction of the relationship between variables.

## Relationship strength

Try to imagine a line that connects the dots in your scatterplot. Is this an easy or difficult task? This task can help you determine the strength of the relationship between your two variables. If your variables have a strong relationship, it will be easy for your to imagine a line connecting all of the dots. For example, in our example scatterplots, the dots seem to go together to form a straight line. However, some scatterplots do not look like this. With some scatterplots, the dots are scattered about so that it is very hard to imagine a line connecting them. The dots are not densely positioned in one place. Instead, they are all over the place. When this is the case, your variables may not have a strong relationship.

## Relationship Direction

You can use your scatterplot to understand the direction of your relationship. Your scatterplot can tell you if you have a positive, negative or zero correlation.

## Positive correlation in a scatterplot

If the line that you imagine in your graph slopes upward from zero, you can conclude that you have a positive correlation between your variables. Increases in one variable are correlated with increases in your other variable. Similarly, decreases in one variable are correlated with decreases in your other variable.

## Negative correlation in a scatterplot

If the line that you imagine in your graph starts high at zero and gradually slopes downward, you can conclude that you have a negative correlation between your variables. Increases in one variable are correlated with decreases in your other variable.

## Zero correlation in a scatterplot

If the line that you imagine does not slop, or you can’t imagine a line at all, you can conclude that you have a zero correlation between your variables. That means that your variables are not related to one another. Increases or decreases in one variable have no effect on increases or decreases in your second variable.

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