**Quantitative Data Analysis 101:**

The lingo, methods and techniques, explained simply.

*By: Derek Jansen (MBA) and Kerryn Warren (PhD) | December 2020*

Quantitative data analysis is one of those things that often **strikes fear** in students. It’s totally understandable – quantitative analysis is a complex topic, full of **daunting lingo**, like medians, modes, correlation and regression. Suddenly we’re all wishing we’d paid a **little** **more** **attention** in math class…

The good news is that while quantitative data analysis is a mammoth topic, gaining a working understanding of the basics isn’t **that hard**, even for those of us who **avoid numbers and math**. In this post, we’ll break quantitative analysis down into **simple**, **bite-sized chunks** so you can approach your research with confidence.

**Overview: Quantitative Data Analysis 101**

**What is quantitative data analysis?**

Despite being a mouthful, quantitative data analysis simply means **analysing data that is numbers-based** – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here.

**What is quantitative analysis used for?**

Quantitative analysis is generally used for three purposes.

- Firstly, it’s used to measure
**differences between groups**. For example, the popularity of different clothing colours or brands. - Secondly, it’s used to assess
**relationships between variables**. For example, the relationship between weather temperature and voter turnout. - And third, it’s used to
**test hypotheses**in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis, which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

**How does quantitative analysis work?**

Well, since quantitative data analysis is all about **analysing numbers**, it’s no surprise that it involves **statistics**. Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty **basic calculations** (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you **don’t need to be** a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

**The two “branches” of quantitative analysis**

As I mentioned, quantitative analysis is powered by **statistical analysis methods**. There are two main “branches” of statistical methods that are used – **descriptive** statistics and **inferential** statistics. In your research, you might **only** use descriptive statistics, or you might use a **mix of both**, depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives. I’ll explain how to choose your methods later.

**So, what are descriptive and inferential statistics?**

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are **population** and **sample**.

First up, **population**. In statistics, the population is the **entire** **group** of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be **all Tesla owners** in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey **every single Tesla owner** in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose **data you actually collect** is called your **sample**.

So, to recap – the population is the **entire group** of people you’re interested in, and the sample is the **subset of the population** that you can actually get access to. In other words, the population is the **full chocolate cake**, whereas the sample is **a slice** of that cake.

**So, why is this sample-population thing important? **

Well, **descriptive** **statistics** focus on describing the **sample**, while **inferential** **statistics** aim to make predictions about the **population, **based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

**Branch 1: Descriptive Statistics**

Descriptive statistics serve a simple but critically important role in your research – to **describe** your data set – hence the name. In other words, they help you understand the details of your **sample**. Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make **inferences** or predictions about the entire population – they’re purely interested in the details of **your specific sample**.

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions, they may be the only type of statistics you use. We’ll explore that a little later.

**So, what kind of statistics are usually covered in this section?**

Some common statistical tests used in this branch include the following:

**Mean**– this is simply the mathematical average of a range of numbers.**Median**– this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.**Mode –**this is simply the most commonly occurring number in the data set.**Standard deviation**– this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average).- In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
- Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.

**Skewness**. As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

**Feeling a bit confused? **Let’s look at a practical example using a small data set.

On the left-hand side is the data set. This details the bodyweight of a sample of 10 people. On the right-hand side, we have the descriptive statistics. Let’s take a look at each of them.

First, we can see that the **mean** **weight** is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the **median** is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the **mode**, there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the **standard deviation**. 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the **skewness** of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some **useful insight** into the data set. Of course, this is a **very small** data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones.

**But why do all of these numbers matter?**

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

- Firstly, they help you get both a
**macro and micro-level view**of your data. In other words, they help you understand both the big picture and the finer details. - Secondly, they help you
**spot potential errors**in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data. - And lastly, these descriptive statistics help
**inform which inferential statistical techniques**you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, **descriptive statistics are really important**, even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

**Don’t be a sucker** – give your descriptive statistics the love and attention they deserve!

**Branch 2: Inferential Statistics**

As I mentioned, while **descriptive** **statistics** are all about the details of your specific data set – your **sample** – **inferential** **statistics** aim to make inferences about the **population**. In other words, you’ll use inferential statistics to make **predictions** about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

- Firstly, predictions about
**differences between groups**– for example, height differences between children grouped by their favourite meal or gender. - And secondly,
**relationships between variables**– for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and **make** **predictions** about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for **hypothesis** **testing** – in other words, to test hypotheses that predict changes or differences.

Of course, when you’re working with inferential statistics, the **composition of your sample** is really important. In other words, if your sample doesn’t accurately represent the population you’re researching, then your findings won’t necessarily be very useful.

For example, if your population of interest is a mix of **50% male** and **50% female**, but your sample is **80% male**, you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post.

**What statistics are usually used in this branch?**

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are **T-Tests**. T-tests **compare the means** (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have **ANOVA, **which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse **multiple groups**, not just two groups So it’s basically a t-test on steroids…

Next, we have **correlation analysis**. This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables **intuitively**, but correlation analysis allows us to measure that relationship **scientifically**.

Lastly, we have **regression analysis** – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand **cause and effect** between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other.

**Stats overload…**

I hear you. To make this all a little more tangible, let’s take a **look at an example** of a correlation in action.

Here’s a scatter plot demonstrating the correlation (relationship) between weight and height. Intuitively, we’d expect there to be some relationship between these two variables, which is what we see in this scatter plot. In other words, the results tend to cluster together in a diagonal line from bottom left to top right.

As I mentioned, these are are **just a handful** of inferential techniques – there are many, many more. Importantly, each statistical method has its own **assumptions** and limitations.

For example, some methods only work with normally distributed (parametric) data, while other methods are designed specifically for non-parametric data. And that’s exactly why **descriptive statistics are so important** – they’re the first step to knowing which inferential techniques you can and can’t use.

**How to choose the right analysis method**

To choose the right statistical methods, you need to think about **two important factors**:

- The
**type**of quantitative data you have (specifically,**level of measurement**and the shape of the data). And, - Your
**research questions and hypotheses**

Let’s take a closer look at each of these.

**Factor 1 – Data type**

The first thing you need to consider is the **type** of data you’ve collected (or the type of data you **will** collect). By data types, I’m referring to the **four levels of measurement** – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out this post which explains each of the four levels of measurement.

**Why does this matter?**

Well, because different statistical methods and techniques **require** different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with **categorical** data (for example, yes/no type questions, or gender or ethnicity), while others work with **continuous** **numerical** data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless. So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here.

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the **shape of your data**. Specifically, does it have a **normal** **distribution** (in other words, is it a bell-shaped curve, centred in the middle) or is it very **skewed** to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

This is another reminder of why **descriptive statistics are so important** – they tell you all about the shape of your data.

**Factor 2: Your research questions**

The next thing you need to consider is your specific **research questions, **as well as your** hypotheses** (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your **sample** (as opposed to the entire population), then **descriptive** **statistics** are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand **differences** **between** **groups** or **relationships** **between** **variables** and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics **and** inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

**Never** shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

**Time to recap…**

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

- Quantitative data analysis is all about
**analysing number-based data**(which includes categorical and numerical data) using various statistical techniques. - The two main
**branches**of statistics are**descriptive statistics**and**inferential statistics**. Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population. - Common
**descriptive statistical methods**include**mean**(average),**median**, standard**deviation**and**skewness**. - Common
**inferential statistical methods**include**t-tests**,**ANOVA**,**correlation**and**regression**analysis. - To choose the right statistical methods and techniques, you need to consider the
**type of data you’re working with**, as well as your**research questions**and hypotheses.

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