What do we mean by descriptive statistics?
With any kind of data, the main objective is to describe a population at large — and using descriptive statistics, researchers can quantify and describe the basic characteristics of a given data set.
For example, researchers can condense large data sets, which may contain thousands of individual data points or observations, into a series of statistics that provide useful information on the population of interest. We call this process “describing data”.
In the process of producing summaries of the sample, we use measures like mean, median, variance, graphs, charts, frequencies, histograms, box and whisker plots, and percentages. For datasets with just one variable, we use univariate descriptive statistics. For datasets with multiple variables, we use bivariate correlation and multivariate descriptive statistics.
Want to find out the definitions?Univariate descriptive statistics: this is when you want to describe data with only one characteristic or attribute
Bivariate correlation: this is when you simultaneously analyze (compare) two variables to see if there is a relationship between them
Multivariate descriptive statistics: this is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable
Then, after describing and summarising the data, as well as using simple graphical analyses, we can start to draw meaningful insights from it to help guide specific strategies. It’s also important to note that descriptive statistics can employ and use both quantitative and qualitative research.
Describing data is undoubtedly the most critical first step in research as it enables the subsequent organisation, simplification and summarisation of information — and every survey question and population has summary statistics. Let’s take a look at a few examples.
Examples of descriptive statistics
Consider for a moment a number used to summarise how well a striker is performing in football — goals scored per game. This number is simply the number of shots taken against how many of those shots hit the back of the net (reported to three significant digits). If a striker is scoring 0.333, that’s one goal for every three shots. If they’re scoring one in four, that’s 0.250.
A classic example is a student’s grade point average (GPA). This single number describes the general performance of a student across a range of course experiences and classes. It doesn’t tell us anything about the difficulty of the courses the student is taking, or what those courses are, but it does provide a summary that enables a degree of comparison with people or other units of data.
Ultimately, descriptive statistics make it incredibly easy for people to understand complex (or data intensive) quantitative or qualitative insights across large data sets.
Types of descriptive statistics
To quantitatively summarise the characteristics of raw, ungrouped data, we use the following types of descriptive statistics:
- Measures of Central Tendency,
- Measures of Dispersion and
- Measures of Frequency Distribution.
Following the application of any of these approaches, the raw data then becomes ‘grouped’ data that’s logically organised and easy to understand. To visually represent the data, we then use graphs, charts, tables etc.
Let’s look at the different types of measurement and the statistical methods that belong to each:
Measures of Central Tendency are used to describe data by determining a single representative of central value. For example, the mean, median or mode.
Measures of Dispersion are used to determine how spread out a data distribution is with respect to the central value, e.g. the mean, median or mode. For example, while central tendency gives the person the average or central value, it doesn’t describe how the data is distributed within the set.
Measures of Frequency Distribution are used to describe the occurrence of data within the data set (count).
The methods of each measure are summarised in the table below:
|Measures of Central Tendency||Measures of Dispersion||Measures of Frequency Distribution|
Mean: The most popular and well-known measure of central tendency. The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.
Median: The median is the middle score for a set of data that has been arranged in order of magnitude. If you have an even number of data, e.g. 10 data points, take the two middle scores and average the result.
Mode: The mode is the most frequently occurring observation in the data set.
Range: The difference between the highest and lowest value.
Standard deviation: Standard deviation measures the dispersion of a data set relative to its mean and is calculated as the square root of the variance.
Quartile deviation: Quartile deviation measures the deviation in the middle of the data.
Variance: Variance measures the variability from the average of mean.
Absolute deviation: The absolute deviation of a dataset is the average distance between each data point and the mean.
Count: How often each value occurs.
Scope of descriptive statistics in research
Descriptive statistics (or analysis) is considered more vast than other quantitative and qualitative methods as it provides a much broader picture of an event, phenomenon or population.
But that’s not all: it can use any number of variables, and as it collects data and describes it as it is, it’s also far more representative of the world as it exists.
However, it’s also important to consider that descriptive analyses lay the foundation for further methods of study. By summarising and condensing the data into easily understandable segments, researchers can further analyse the data to uncover new variables or hypotheses.
Mostly, this practice is all about the ease of data visualisation. With data presented in a meaningful way, researchers have a simplified interpretation of the data set in question. That said, while descriptive statistics helps to summarise information, it only provides a general view of the variables in question.
It is, therefore, up to the researchers to probe further and use other methods of analysis to discover deeper insights.
Things you can do with descriptive statistics:
- Define subject characteristics: If a marketing team wanted to build out accurate buyer personas for specific products and industry verticals, they could use descriptive analyses on customer datasets (procured via a survey) to identify consistent traits and behaviours.
They could then ‘describe’ the data to build a clear picture and understanding of who their buyers are, including things like preferences, business challenges, income and so on.
- Measure data trends
Let’s say you wanted to assess propensity to buy over several months or years for a specific target market and product. With descriptive statistics, you could quickly summarise the data and extract the precise data points you need to understand the trends in product purchase behaviour.
- Compare events, populations or phenomena
How do different demographics respond to certain variables? For example, you might want to run a customer study to see how buyers in different job functions respond to new product features or price changes. Are all groups as enthusiastic about the new features and likely to buy? Or do they have reservations? This kind of data will help inform your overall product strategy and potentially how you tier solutions.
- Validate existing conditions
When you have a belief or hypothesis but need to prove it, you can use descriptive techniques to ascertain underlying patterns or assumptions.
- Form new hypotheses
With the data presented and surmised in a way that everyone can understand (and infer connections from), you can delve deeper into specific data points to uncover deeper and more meaningful insights — or run more comprehensive research.
Guiding your survey design to improve the data collected
To use your surveys as an effective tool for customer engagement and understanding, every survey goal and item should answer one simple, yet highly important question:
“What am I really asking?”
It might seem trivial, but by having this question frame survey research, it becomes significantly easier for researchers to develop the right questions that uncover useful, meaningful and actionable insights.
Planning becomes easier, questions clearer and perspective far wider and yet nuanced.
Hypothesise — what’s the problem that you’re trying to solve? Far too often, organisations collect data without understanding what they’re asking, and why they’re asking it.
Finally, focus on the end result. What kind of data do you need to answer your question? Also, are you asking a quantitative or qualitative question? Here are a few things to consider:
- Clear questions are clear for everyone. It takes time to make a concept clear
- Ask about measurable, evident and noticeable activities or behaviours.
- Make rating scales easy. Avoid long lists, confusing scales or “don’t know” or “not applicable” options.
- Ensure your survey makes sense and flows well. Reduce the cognitive load on respondents by making it easy for them to complete the survey.
- Read your questions aloud to see how they sound.
- Pretest by asking a few uninvolved individuals to answer.
As well as understanding what you’re really asking, there are several other considerations for your data:
- Keep it random
How you select your sample is what makes your research replicable and meaningful. Having a truly random sample helps prevent bias, increasingly the quality of evidence you find.
- Plan for and avoid sample error
Before starting your research project, have a clear plan for avoiding sample error. Use larger sample sizes, and apply random sampling to minimise the potential for bias.
- Don’t over sample
Remember, you can sample 500 respondents selected randomly from a population and they will closely reflect the actual population 95% of the time.
- Think about the mode
Match your survey methods to the sample you select. For example, how do your current customers prefer communicating? Do they have any shared characteristics or preferences? A mixed-method approach is critical if you want to drive action across different customer segments.
Use a survey tool that supports you with the whole process
Surveys created using a survey research software can support researchers in a number of ways:
- Employee satisfaction survey template
- Employee exit survey template
- Customer satisfaction (CSAT) survey template
- Ad testing survey template
- Brand awareness survey template
- Product pricing survey template
- Product research survey template
- Employee engagement survey template
- Customer service survey template
- NPS survey template
- Product package testing survey template
- Product features prioritisation survey template
These considerations have been included in Qualtrics’ survey software, which summarises and creates visualisations of data, making it easy to access insights, measure trends, and examine results without complexity or jumping between systems.
Uncover your next breakthrough idea with Stats iQ™
What makes Qualtrics so different from other survey providers is that it is built in consultation with trained research professionals and includes high-tech statistical software like Qualtrics Stats iQ.
With just a click, the software can run specific analyses or automate statistical testing and data visualisation. Testing parameters are automatically chosen based on how your data is structured (e.g. categorical data will run a statistical test like Chi-squared), and the results are translated into plain language that anyone can understand and put into action.
- Get more meaningful insights from your data
Stats iQ includes a variety of statistical analyses, including: describe, relate, regression, cluster, factor, TURF, and pivot tables — all in one place!
- Confidently analyse complex data
Built-in artificial intelligence and advanced algorithms automatically choose and apply the right statistical analyses and return the insights in plain english so everyone can take action.
- Integrate existing statistical workflows
For more experienced stats users, built-in R code templates allow you to run even more sophisticated analyses by adding R code snippets directly in your survey analysis.
Advanced statistical analysis methods available in Stats iQ
Regression analysis – Measures the degree of influence of independent variables on a dependent variable (the relationship between two or multiple variables).
Analysis of Variance (ANOVA) test – Commonly used with a regression study to find out what effect independent variables have on the dependent variable. It can compare multiple groups simultaneously to see if there is a relationship between them.
Conjoint analysis – Asks people to make trade-offs when making decisions, then analyses the results to give the most popular outcome. Helps you understand why people make the complex choices they do.
T-Test – Helps you compare whether two data groups have different mean values and allows the user to interpret whether differences are meaningful or merely coincidental.
Crosstab analysis – Used in quantitative market research to analyse categorical data – that is, variables that are different and mutually exclusive, and allows you to compare the relationship between two variables in contingency tables.
Go from insights to action
Now that you have a better understanding of descriptive statistics in research and how you can leverage statistical analysis methods correctly, now’s the time to utilise a tool that can take your research and subsequent analysis to the next level.
Try out a Qualtrics survey software demo so you can see how it can take you through descriptive research and further research projects from start to finish.