Quantitative Data Analysis 101

Quantitative analysis is where a lot of otherwise solid dissertations come unstuck. Run a test your data can’t support, and your findings won’t survive your committee’s first question, however carefully you collected them.

Having helped thousands of students through their analysis, we’ve found the statistics themselves are rarely the problem. The hard part is knowing which ones to use and why. In this post, we’ll explain the two branches of quantitative analysis in plain language, show you how to choose a test, and walk through how three real dissertations reported and justified theirs.

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What is quantitative data analysis?

Quantitative data analysis means analyzing data that is numbers-based, or data that can be converted into numbers without losing its meaning.

For example, category-based variables like gender, ethnicity or native language can be coded as numbers (English = 1, French = 2, and so on) without losing any information.

This contrasts with qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If that’s closer to your project, our guide to qualitative data analysis methods covers the main approaches.

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes, and your study will usually involve at least one of them:

Whatever the purpose, quantitative analysis runs on statistics, from basic calculations such as averages and medians to more sophisticated analyses such as correlation and regression. You don’t need to be a statistician to use them well, and we’ll explain each one in plain language below.

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The two “branches” of quantitative analysis

The statistical methods behind quantitative analysis fall into two main branches: descriptive statistics and inferential statistics. Depending on your research questions, aims and objectives, you might use only descriptive statistics, or a mix of both. We’ll explain how to choose later on.

“So, what are descriptive and inferential statistics?”

To understand the difference, you first need two words: population and sample.

In statistics, the population is the entire group of people (or animals, or organizations) you’re interested in. For example, if you were researching Tesla owners in the US, then the population would be every Tesla owner in the US.

You’re very unlikely to be able to interview or survey every one of them. Realistically, you might reach a few hundred, or a few thousand, through an online survey. This smaller group, whose data you actually collect, is your sample. Think of the population as the whole chocolate cake and your sample as a slice of it.

Here’s why that matters. Descriptive statistics describe the sample, while inferential statistics use the sample to draw conclusions about the population. One branch investigates the slice; the other tells you what the slice suggests about the whole cake.

Branch 1: Descriptive statistics

Descriptive statistics have a simple but important job: to describe your data set, hence the name. Unlike inferential statistics, they don’t try to say anything about the wider population. They’re only interested in the details of your sample.

When you write up your analysis, descriptive statistics come first, before any inferential statistics. Depending on your research questions, they may be the only statistics you need. For example, if your research question only asks how satisfied the students in your survey are with online lectures, means and percentages may answer it completely.

“So, what goes into the descriptive statistics?”

The most common measures are these:

• Mean: the mathematical average of a set of numbers.
• Median: the middle number when the numbers are arranged in order. With an odd count, it’s the middle value; with an even count, it’s halfway between the two middle values.
• Mode: the number that occurs most often in the data set.
• Standard deviation: how spread out the numbers are around the mean. When most numbers sit close to the mean, the standard deviation is low; when they’re scattered widely, it’s high.
• Skewness: how symmetrical the numbers are. Are they spread evenly on both sides of the middle, or do they trail off further to the left or the right?

To make these concrete, here’s a small data set: the body weight of ten people.

Person	Weight (kg)
1	70
2	55
3	90
4	75
5	66
6	73
7	80
8	58
9	76
10	81

And here are its descriptive statistics, with the Excel function that calculates each one:

Statistic	Result	Excel function
Mean	72.4	=AVERAGE
Median	74	=MEDIAN
Standard deviation	10.6	=STDEV.S
Variance	113.2	=VAR.S
Skewness	-0.22	=SKEW

The mean weight is 72.4 kg: the average across the sample.

The median (74 kg) sits a little above the mean, because the lowest weights (55 and 58 kg) pull the average down. The skewness of -0.22 says the same thing: the data are slightly negatively skewed, with a short tail toward the lower values.

There’s no mode, because every weight appears only once. If two people both weighed 65 kg, the mode would be 65.

The standard deviation of 10.6 shows quite a wide spread: the weights run from 55 to 90 kg. The variance (113.2) is simply the standard deviation squared, so it tells you the same thing in squared units.

Keep in mind that ten records is a very small data set, so you can’t read much into these numbers, and this isn’t a full list of descriptive statistics, just the most common ones.

“But why do these numbers matter?”

Descriptive statistics are basic, but they matter for three reasons:

• They give you both a big-picture and a detailed view of your data.
• They help you spot errors in the data. An average far higher than you’d expect, or wildly varied answers to one question, is a sign to double-check (there’s a walkthrough of five common analysis mistakes on our channel).
• They tell you which inferential tests you can use, because many of those tests depend on the shape of your data.

All too often in our coaching sessions, we see students skim over the descriptives in their hurry to get to the inferential tests, and end up with flawed results. Give your descriptive statistics the attention they deserve.

In a dissertation or thesis, descriptive statistics usually come with a sentence saying what they mean. The education PhD from Purdue below surveyed students about their sense of belonging at university, using five-point rating scales:

Notice the pattern: the scale is explained first, then the number (M for mean, SD for standard deviation), then what it means in plain words. Report your own descriptives the same way, so your reader never has to interpret a number on their own.

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Branch 2: Inferential statistics

While descriptive statistics are about your sample, inferential statistics draw conclusions about the population. You use them to estimate what you’d expect to find in the full population, based on what you observed in your sample.

Researchers most often use inferential statistics to look for two things:

• Differences between groups, such as height differences between children grouped by their favorite meal.
• Relationships between variables, such as the relationship between body weight and the number of hours a week a person does yoga.

Because they test whether a pattern in your sample is likely to hold in the population, inferential statistics are what you use for hypothesis testing: checking whether your data support a research hypothesis.

When you’re working with inferential statistics, the composition of your sample really matters. If your sample doesn’t represent the population you’re researching, your conclusions about that population won’t hold. For example, if your population is 50% men and 50% women but your sample is 80% men, you can’t simply generalize from it. Choosing a representative sample is a topic of its own, covered in our guide to sampling methods.

“What tests are usually used in this branch?”

There are many inferential methods, far too many to cover here, so we’ll focus on the five you’re most likely to meet.

T-tests compare the means (averages) of two groups to assess whether they’re significantly different. For example, you might compare the mean blood pressure of a group that took a new medication with that of a group that didn’t.

ANOVA, short for analysis of variance, also compares means, but across three or more groups at once. Think of it as a t-test for more than two groups.

Chi-square tests work with categories rather than numbers. They test whether two categorical variables are related, such as whether people’s preferred brand differs between age groups.

Correlation measures the relationship between two variables: when one goes up, does the other tend to go up, go down, or stay the same? For example, when the average temperature rises, do ice cream sales rise too? We’d expect them to, intuitively, but correlation lets you measure the relationship rather than assume it.

Regression goes a step further than correlation. It models how one or more variables relate to an outcome, so you can predict the outcome’s value from the others. What regression can’t do on its own is prove cause and effect. Two variables can move together because a third one drives both, so causal claims depend on your research design (a controlled experiment, for example), not on the statistic.

To make the concept of correlation a little more concrete, here’s an example with a positive relationship: as height increases, weight tends to increase too.

Inferential results follow a standard shape in a write-up: the test, its statistic, the p-value, often an effect size, and a sentence saying what it means. The psychology PhD from Purdue quoted next tested whether people remember words better when they make up their own memory cues. Its 283 participants each studied words under three cue conditions, so watch how the analysis first asks whether the conditions differ at all, then which ones:

The ANOVA answers “is there a difference among the three?”, and the t-tests then answer “which pairs differ?”. Because the same people took part in all three conditions, the ANOVA is a repeated-measures one: the version for comparing the same people under different conditions.

The ηp² at the end of the ANOVA result is an effect size, showing how big the difference is, which the p-value on its own doesn’t tell you. Notice, too, that the paragraph states its result in words before the numbers back it up. That’s the order to use in your own results chapter.

Every inferential test comes with assumptions and limitations. Some tests, called parametric tests, assume your data are roughly normally distributed; non-parametric tests don’t. That’s exactly why descriptive statistics come first: they tell you which inferential tests your data can support.

For a closer look at this branch, our inferential statistics tutorial covers the key concepts and the steps to get right before you run a test:

How to choose the right analysis method

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

1. The type of quantitative data you have (specifically, its level of measurement and its shape).
2. Your research questions and hypotheses.

Let’s take each in turn.

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Factor 1 – Data type

The first thing to consider is the type of data you’ve collected, or will collect. By data type, we mean the four levels of measurement: nominal, ordinal, interval and ratio. Each level adds one property to the one before it, and the more properties your data have, the more tests you can use:

If you’d like more depth, our explainer on nominal, ordinal, interval and ratio data covers each level with examples.

“Why does this matter?”

Because different statistical methods require different types of data. Some work with categorical data (yes/no answers, gender or ethnicity), others with continuous numerical data (age, weight or income), and some with both.

Run a method on a data type it doesn’t support, and your results will be largely meaningless. So be clear about which types of data you have. Once you are, the University of California, Los Angeles has a useful table showing which statistical tests suit which data types.

If you haven’t collected your data yet, you should ideally work in reverse: decide which analysis would answer your questions, then design your data collection to produce the data that analysis needs. This approach will ensure you achieve strong alignment between your aims and your methods, which is exactly what your committee is looking for.

The other thing to check is the shape of your data. Is it normally distributed (a bell-shaped curve centered in the middle), or skewed to the left or the right? Parametric tests assume roughly normal data; non-parametric tests are designed for data that aren’t. With larger samples, parametric tests cope reasonably well with mild skew, so mild skew alone isn’t a reason to switch. This is another reason descriptive statistics matter: they tell you the shape of your data.

Dissertations that use non-parametric tests usually say why, as the public health PhD from Hungary below does. It screened pregnant women for depression using the Edinburgh Postnatal Depression Scale (EPDS), with very different numbers of women at each stage of pregnancy. Its justification takes three sentences:

As you can see, the passage names the choice, gives the reason in terms of the data’s shape, adds a second reason (unequal group sizes) and tells the reader what the results will look like. If your data push you toward non-parametric tests, justify them the same way.

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Factor 2: Your research questions

The next thing to consider is your research questions, along with your hypotheses if you have any. They largely decide which statistical methods you should use.

If you only want to understand your sample (as opposed to the population), descriptive statistics are probably all you need.

If you want to test differences between groups or relationships between variables, and generalize to the population, you’ll need inferential statistics as well as descriptive ones.

Putting the two factors together, here’s how the most common questions map to tests. The middle column assumes numerical, roughly normal data; the right-hand column is the alternative when the data are ordinal or not normally distributed:

What you want to know	Numerical, normal data	Ordinal or non-normal data
Do two separate groups differ?	Independent-samples t-test	Mann-Whitney U test
Do the same people differ at two points?	Paired t-test	Wilcoxon signed-rank test
Do three or more separate groups differ?	One-way ANOVA	Kruskal-Wallis test
Are two numerical variables related?	Pearson correlation	Spearman correlation

If the same people are measured three or more times, as in the psychology PhD above, the repeated-measures ANOVA takes the one-way ANOVA’s place, with the Friedman test as its non-parametric alternative.

The flowchart below walks through the same decision step by step, and adds the two cases the table leaves out: an outcome that’s a category (a chi-square test) and predicting an outcome from other variables (regression).

So get clear on your research aims, questions and hypotheses before you look at any statistical techniques. Never shoehorn a technique into your study because you like it or have used it before. Your methods must fit your data and your questions.

If you’d like someone to check that your analysis plan fits your data before you run it, book a free chat with one of our coaches. We’ll talk through your study and where your analysis needs work.

Still have questions?

What is quantitative data analysis?

Quantitative data analysis is the use of statistics to make sense of number-based data, such as test scores, survey ratings or measurements. It has two branches: descriptive statistics, which summarize the data you collected, and inferential statistics, which use that sample to draw conclusions about a wider population.

What is an example of quantitative analysis?

Comparing the exam scores of two classes taught in different ways is a simple example. You’d first describe each class with its mean and standard deviation, then use an independent-samples t-test to check whether the difference between the two means is larger than you’d expect by chance.

What are the main types of quantitative analysis?

The two main types are descriptive analysis, which summarizes your data with measures like the mean and standard deviation, and inferential analysis, which tests whether patterns in your sample hold in the population. Inferential tests split again into tests of difference, such as t-tests and ANOVA, and tests of relationship, such as correlation and regression.

Can I use ChatGPT to analyze my data?

You can use AI tools to explain a test or check your understanding, but the analysis, and your account of it, have to be your own work. Universities differ on whether and how AI may be used in a dissertation, and some require you to declare it, so check your program’s AI policy first. Never paste confidential or identifiable research data into a public AI tool, since that may breach the terms of your ethics approval.

How do I know which statistical test to use?

Start with your research question: are you comparing groups or looking at a relationship? Then check your data: how many groups you have, whether the outcome is numerical or categorical, and whether it’s normally distributed. For example, two separate groups with normal numerical data call for an independent-samples t-test; with non-normal data, a Mann-Whitney U test.

What are some examples of quantitative data?

Quantitative data is anything recorded as a number or coded as one. Examples include exam scores, ages, incomes, heart rates, reaction times, the number of hours spent studying, and survey answers on a rating scale, such as satisfaction scored from 1 to 5. Categories such as gender or country can be analyzed quantitatively too, once each category is coded as a number.

How do you analyze data in quantitative research?

Most quantitative analyses follow the same sequence. Clean your data and check for errors, then run descriptive statistics to summarize it and see its shape. Next, check the assumptions of the test that fits your research question, run that inferential test, and report the result with its statistic, its p-value, an effect size where you can, and a plain-English sentence saying what it means.

What software can I use for quantitative analysis?

Excel handles descriptive statistics and, through its Analysis ToolPak add-in, basic tests such as t-tests, ANOVA, correlation and regression, but not non-parametric tests. SPSS is common in the social sciences, and R and Python are free and powerful but take longer to learn. JASP and jamovi are free point-and-click options. Check what your department supports before you choose.

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