Last Updated on 12 September 2023

When we first encounter a dataset, it’s tempting to assume that it’s normal. After all, we are accustomed to seeing distributions that look like this:

However, this is not always the case. There are many situations where a data set will appear to be normally distributed but is actually skewed towards one end or the other without being completely non-normal (e.g., positively or negatively). This happens when you’re working with small sample sizes or when there is an extreme outlier in your data set which skews the average value upwards or downwards dramatically. In both cases, it can make sense not even bother trying any statistical tests if your data is not (really) normal because they won’t be accurate anyway!

## What is Assumption of Normality?

This is a statistical assumption that your data is drawn from a normal distribution. This means that your data has been randomly sampled from a larger population, and the sample size is large enough.

A normal distribution is a bell-shaped curve, with most values concentrated around the mean (average) value, while fewer values are further away from this point on either side (or tails). The shape of this curve allows us to use probability theory to make predictions about future events based on past ones — for example: if we know how many people have died due to an earthquake in Nepal over time, we can predict how many will die during future earthquakes using our knowledge about how earthquakes affect different areas at different times.

Normal distributions also play an important role when calculating confidence intervals or p-values (p = probability).

## Assumption of Normality vs. Assumption of Homogeneity

Let’s start with a quick overview of the two assumptions. The first, assumption of normality, is about the distribution of your data. For example, if a researcher wants to test whether men and women differ in their average height and weight (and they do!), then they need to know that both groups’ heights are normally distributed around some mean value (in this case 5’9″ for men and 5’4″ for women).

The second assumption–assumption of homogeneity–is about how different groups compare relative to each other on some outcome variable (like height). In other words: Are there any differences between your subgroups? If so, how do those differences compare?

If you think about it, this is a pretty tall order. You want to know whether the different groups (e.g., men and women) are really different from each other on some outcome variable (like height), but you also want to know how those differences compare relative to each other (in this case, men are taller than women).

The problem with these two assumptions is that they are often violated in practice. For example, imagine you had a group of people who were trying to predict the outcome of a coin flip (heads or tails). You asked them all to estimate their own chances (or give their best guess) and then collected those estimates into one big data set.

## Why it’s important to understand Assumption of Normality

It’s an important concept to understand because otherwise it can lead to bad conclusions. If you’re analyzing data and assuming that your sample is normally distributed, but it isn’t, then the results of your analysis will be wrong. You might think that people who buy more organic foods are healthier than those who don’t–but if your sample has an abnormally high percentage of sick people (because they all buy organic), then this conclusion would be incorrect!

You also can’t use statistical tests that assume the data is normally distributed if it isn’t; these tests include things like t-tests and ANOVAs. And finally: even if everything looks fine on paper and in theory…you still won’t know anything until you get out there into real life with real people doing real things!

## Why is it not okay to assume the data you are working with is normally distributed?

As we have discussed, the assumption of normality can be useful in many situations. However, it is not always a good idea to assume that your data will follow a normal distribution. While there are ways around this problem (such as using empirical probability distributions), it’s important to know why this assumption is not ideal before you begin thinking about how best to deal with it.

The first thing you should understand is that making assumptions about your data will interfere with its accuracy and reliability–and perhaps even lead you down the wrong path altogether! If you’re working with a set of numbers and trying to use them for something important (like making predictions), then being able to trust those numbers is essential. You don’t want any doubt in their validity because that could cause problems later on down the line when they are used as evidence or support for other claims (or conclusions). And while there may be some situations where assuming normality isn’t harmful enough that we’d worry too much about whether our assumptions were correct or not (e.,g., when calculating averages), these situations are few and far between compared against all other cases where such assumptions would lead us astray from reality.”

## When is it okay to assume the data you are working with is normally distributed?

When you’re working with a large sample size and/or a known population, it is okay to assume that your data is normally distributed. This is because:

- You can be confident that your sample will represent the population well (if it doesn’t, then there’s probably something wrong with how you collected or analyzed the data).
- If you’re working with data from a census or survey of students at your school, then these are both examples of known populations–you know exactly what kind of distribution they should have because everyone counts as one unit in this case!

## Don’t always assume normality

When you’re presented with a dataset, always check if it’s (really) normal before going further. The importance of checking the data you are working with cannot be overstated. When testing for normality, one must be aware of what assumptions they are making and how to check if those assumptions are met or not.

The most common way to test for normality is by using the Shapiro-Wilk test statistic which can be calculated using R or Python libraries like scipy and numpy . If this is less than 1 or greater than 6 in absolute value then there is evidence against the null hypothesis that your sample came from a normal distribution (this will be true even if all other conditions hold). In such cases, it’s best to try another approach!

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