Association is what correlation really means. It measures to what extent there is a relationship between 2 variables. It is a statistical measurement of the way 2 variables relate where positive correlation ranges from positive one (+1) to negative one (-1). A correlation of zero indicates that between the variables, there is no relationship. A correlation of negative 1 also indicates a perfect correlation that is negative, which means that as one of the variables go up, the other one goes down. A positive one correlation indicates a perfect correlation that is positive, which means that together, both variables move in the same direction. You can visually express a correlation. You can do this by drawing scatter grams or scatter plots, which are graphs where you can plot a variable’s figures and compare this to the other figures on a different graph. Here is a course entitled Introductory Statistics that shows you applications, calculations and concepts of various statistics data that you can learn according to your own pace.

The extent to which one variable relates to another is a central research question. For example, does student academic achievement have a correlation to socioeconomic status? What is the relationship between earnings and education? These and other questions wonder whether there is an existing correlation between a couple of variables. When there is an existing correlation, a change in 1 of the variables is related with changes in another. Here is an article entitled Statistics Formula: Mean, Median, Mode and Standard Deviation that deals with analyzing all sorts of data that you might be interested in.

To find out if 2 variables have an effect on one another, you can enter your data into a spread sheet. For example, if you want to find out if a correlation exists between the number of hours you tutor or math test scores for a group of twenty kids. On your spread sheet, enter the number of hours of tutoring per student in one column and the scores on the math test on another. Get the tutoring hours mean number by adding all the hours and dividing by the number of students (20). Next, add all the math scores and divide this by 20 as well. Plot your data visually using a scatter plot. Many programs offering spread sheets such as Excel let you display graphical data. You can do this by clicking ‘insert’ and then selecting ‘scatter plot.’ Excel will then display scatter plots that show your data on the axes points for x and y. For the example, let X= #tutoring hours and Y=math scores. Plot each student’s scores and notice how the dots look. Once you see the dots going upwards in the same direction, this is an indication that the correlation is positive. Here is a course entitled Optimization and A/B Testing Statistics that helps raise your skill level in terms of a/b testing and hypothesis testing.

Other examples of a positive correlation are:

- The more education years you complete, the higher your potential to earn.
- The less time you spend doing business marketing, the fewer new clients you get.
- The more time you invest money, the more compound interest it earns.
- The money you save, the more secure you feel financially.

## Perfect Positive Correlations Example

Are perfect positive correlations the same as a positive correlation? Not really. Positive correlations mean that there is indeed a relationship between 2 variables. However, unlike a positive correlation, a *perfect* positive correlation gets the value of 1. When there is absolutely no correlation, i.e., one variable has absolutely nothing to do with another one, the value is 0. If there is a correlation but it is perfectly negative, the value is -1. The closer the number is to either -1 or 1, the stronger the correlation. So something might have a value of .77. This is a positive, but not perfect correlation. Perfect positive correlations mean that one hundred per cent of the time, the relationship that looks like it exists between 2 variables is positive. An example of a perfect positive correlation is when comparing the number of people who go to see a movie and the total spent money on tickets, when plotted on a graph, it equals to 1. This means that every time a number of people (x) go, an amount of money (y) is spent without variation on the tickets:

## Positive Correlation Example #1: Sales in Ice Cream

The ice cream shop around the corner tracks the temperature for each day and how much ice cream they sell. Here are their numbers for the last week and a half:

Temperature vs Sales in Ice Cream

Temperature in ˚C | Sales |

17.2 ˚C | $408 |

22.6 ˚C | $445 |

18.1 ˚C | $421 |

23.4 ˚C | $544 |

25.1 ˚C | $614 |

19.4 ˚C | $412 |

22.1 ˚C | $522 |

18.5 ˚C | $406 |

15.2 ˚C | $332 |

11.9 ˚C | $185 |

16.4 ˚C | $325 |

14.2 ˚C | $215 |

On a scatter plot, here is the same data:

You can see that more sales occur during warmer weather. This is a good correlation but not perfect.

## Positive Correlation Example #2

During the months of March and April, the number of strawberry jam jars sold weekly at a New York local market was taken down. In the same frame of time, the number of copies of a popular CD that played classical music was sold in Texas was recorded. The data was plotted and examined:

The # of CD’s sold in Texas | The number of strawberry jam jars sold in New York |

56 CDs | 12 jars |

52 CDs | 11 jars |

48 CDs | 11 jars |

42 CDs | 10 jars |

35 CDs | 9 jars |

30 CDs | 7 jars |

25 CDs | 5 jars |

On a scatter gram, here is what it this positive correlation looks like:

From just observing the graph, you will see that there are high positive correlations between the 2 data sets. Does this mean that the strawberry jam jars sold in New York was causing an increase in the CD’s sold in Texas? Naturally this is not the case! Remember that you need to be extra careful when making an analysis in statistics, and that correlation in no way means causation. By the way here is a course called Practical Statistics for the User Experience that is an online practical course for using statistics in a manner that is quite approachable and with loads of examples.

## Positive Correlation Example #3

The company physician was looking into the possible effects of stress upon the company management employees’ health. He thinks that stressed out employees will have higher systolic blood pressure. On 10 employees aged thirty-five to fifty-five, a random sample is taken and takes down this information:

Employee | Systolic Blood Pressure (Y) | Age (X) |

1 | 133 | 37 |

2 | 143 | 39 |

3 | 135 | 42 |

4 | 151 | 44 |

5 | 143 | 47 |

6 | 158 | 48 |

7 | 163 | 50 |

8 | 146 | 51 |

9 | 168 | 52 |

10 | 160 | 54 |

With this data, a scatter graph is plotted:

This graph shows the relationship between age and blood pressure. It appears that the older the age, the higher the blood pressure. It can then be said that these 2 variables have a positive correlation. In this example, the data are sets or pairs of 2 variables’ values: blood pressure and age.

## Positive Correlation Example #4

How much money did Matthew earn each week working at his dad’s store? In this graph, the weeks are plotted on the x axis and the paychecks on the y axis. Generally, the variables that are not influences by anything is called the independent variable. In this case, it is his being employed at his dad’s store. On the x axis, the dependent variable which is the one affected by the independent variable is plotted. In this case, it is Matthew’s paycheck.

In the graph, you will see that in a period of 2 weeks, he earned about one hundred twenty-five dollars and on the eighteenth week, he earned about one hundred sixty-five. The trend of the data is what you are looking at here. For instance, with this set of data, it can clearly be seen that he is earning more as each week goes by, making this an example of a positive correlation.

## And Now A Note on Positive Correlation Limitations

Correlations do not let you go beyond the given data. For instance, suppose you found a relationship between the number of GCSE passers ( one to six) and the time spent on homework (half an hour to three hours). Making inferences from this that spending six homework hours would give you more of a likelihood of passing GCSE is not legitimate.

Also, correlation is not and should be taken to mean causation. Even if there are strong associations between both variables in a graph, you can’t assume that one is caused by the other. For instance, you found a positive correlation between watching TV shows that were violent and adolescent violent behavior. The cause of this may be a 3^{rd} variable which is extraneous. For example, it could be genetic or having grown up in a home where violent behavior was okay. Here is course entitled Workshop in Probabilty and Statistics that teach you statistics fundamentals and how to make sense of varying information.