When you’re studying statistics, it’s likely that you already heard about variance. After all, this is one of the first concepts you learn. 

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What is Variance?

Variance is simply a measurement of the spread between numbers in a data set. So, you can say that variance measures how far each number in a data set is from the mean as well as from all the other numbers in your data set. 

Understanding Variance

Now that you already know what variance is, you also need to learn how to calculate it. 

Understanding variance analysis.

So, when you want to calculate variance, you need to take the differences between each number in the data set and the mean, and then square the difference to make them positive. Finally, you still need to divide the sum of squares by the number of values in your dataset. If this sounds too complicated, you can relax because the formula you need to use is pretty straightforward. 

Variance’s Formula 

Where:

xi​ = refers to the ith data point

xˉ = refers to the mean of all data points

n = refers to the number of data points​

One of the things that you also need to keep in mind is that variance and the standard deviation are very close. After all, the square root of the variance is the standard deviation (σ).

Learn more about the standard deviation.

How To Use Variance

Ultimately, the variance measures the variability from the mean or average and it can be used for a wide range of things. For example, if you’re an investor, you may be used to use variance even though you may have not realized it yet. Ultimately, variability is volatility, and volatility is a measure of risk. Therefore, the variance statistic can help determine the risk an investor assumes when purchasing a specific security.

When you have a large variance, it means that the numbers in the data set are far from the mean as well as far from each other. On the other hand, when you have a small variance, it means that the numbers in the data set are close to the mean as well as close to each other. When you have a variance that is equal to zero, it means that all values within your data set are identical. 

Note that variances are always positive or zero. There can’t be a negative variance. 

What is a confidence interval?

Advantages And Disadvantages Of Using Variance

In statistics, researchers use variance to know how individual numbers relate to each other within a data set. 

One of the main limitations of variance is the fact that it gives added weight to outliers. In case you don’t know, outliers are the numbers that are far from the mean. But when you square these numbers, you can skew the data. 

On the other hand, one of the biggest advantages of using variance is the fact that it treats all deviations from the mean exactly the same way regardless of their direction. The squared deviations cannot sum to zero and give the appearance of no variability at all in the data.

You should also keep in mind that interpreting variance is not always easy.

It is normal that when you are studying statistics, you want to compare different groups to see if there are differences. Well, in order to do so, you need to use variance analysis. 

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Looking At The Variance Analysis Basics

As we already mentioned above, variance analysis involves comparing what is expected and what is actually observed. After all, if you recall, the variance is the difference between the observed values and the model values. 

So, when you have univariate data, your models will be the measures of central tendency. On the other hand, in the case of simple correlations or bivariate data, this would mean that the difference between the line of best fit and the actual values measured. 

However, it’s important to consider that in the case of multivariate data, which is three of more variables, the challenge increase. This is because you are comparing an empirical model to a theoretical model. So, as you can easily understand, the easiest way to do this is to compare groups to an outcome. But the number of groups and variables determines the best method to use. 

What is the F distribution?

Comparing Two Groups

Comparing two groups to a single outcome is the simplest thing you can do. In this case, you need to use the t-test that compares the same outcome for two groups. The main benefit of using the t test is that you can do it in two different ways:

• A Dependent T-Test: Compares the same outcome for 2 groups with the same participants. This is usually the one you should pick for before and after scenarios. 
• An Independent T-Test: Compares 2 groups based on the same outcome. This is the type of test that is more common in experimental studies.

Discover what to do when you can’t run the ideal analysis.

Comparing Multiple Groups

One of the great things about statistics is that you have numerous ways to look at your data. So, as you can imagine, in statistics, you can also compare 3 or more groups. While it takes more time, it is certainly useful. 

While you could use t tests, the truth is that they’re not the best option. After all, each t-test has error associated with it, so doing multiple t-tests only increases the amount of error. Instead, you need to use the special technique, analysis of variance or ANOVA.

Discover everything you need to know about statistical significance.

Analysis Of Variance (ANOVA)

When you are using this method, instead of analyzing the variance of 2 groups, you will be analyzing the variance and the error that occurs in a group or between groups. So, we can then state that it compares the groups in the context of a single outcome. 

You need to keep in mind that you will analyze the variance using the F ratio which is the ratio of the error variance between the groups compared to the error variance within the group. 

Just like the t-test, the F-ratio compares actual values to a distribution values that helps to determine significance. In this way, you can see if there is a significant difference between the groups.

Notice that the F-test only reveals if there is a significant difference. It does not determine which group is different nor how it is different. For that, you need post hoc tests.