Beyond the numbers: understanding statistics through Tableau

This article explores the critical role of statistics in data analysis and how Tableau can facilitate understanding complex concepts through visualisation.

Introduction

In the information age we live in, data is everywhere. From business decisions to scientific advances, the ability to interpret and analyse data has become a fundamental skill. But what makes this interpretation possible? The answer lies in statistics, the branch of mathematics that allows us to collect, analyse, interpret, present, and organise data. Despite its importance, statistics can seem intimidating to many, given its complexity and the need for deep understanding to apply it correctly.

This is where Tableau comes in, a revolutionary tool in the field of data analysis. With its intuitive interface and powerful visualisation capabilities, Tableau transforms complex numbers and intricate datasets into understandable and interactive charts. This not only makes data analysis accessible to a wider audience, but also facilitates the discovery of patterns, trends, and anomalies that would otherwise remain hidden.

This article aims to guide readers through the fundamental concepts of statistics, illustrating them with practical examples in Tableau. Whether you are an experienced data analyst or a beginner in the world of data, the goal is to demystify statistics and show how, with the right tools, it can become a valuable resource rather than an obstacle.

Through a series of concrete examples, we will explore the different types of data, how to interpret fundamental measures in datasets, the meaning of distributions, and how visualisation can play a key role in making statistics not only more accessible, but also more engaging. We will lay the groundwork so that even more advanced concepts, such as hypothesis testing and analysis of variance, become not only understandable, but also applicable in your daily data analysis.

With the advent of tools like Tableau, the barrier to entry for data analysis is significantly lowered. This article aims to be a testament to how statistics, far from being an abstract and distant subject, is actually a vibrant and fundamental discipline, capable of shaping the way we understand the world through data. Let us begin this visual journey, discovering how data can tell stories, guide decisions, and ultimately improve our understanding of the world.

Note: By clicking on each image, you can access the dashboard available on my personal Tableau Public page.

Types of variables

This topic forms the foundation for understanding how data can be collected, analysed, and interpreted. In this section, we will emphasise the distinction between discrete and continuous variables, illustrating how each of these can be represented and analysed in Tableau.

Statistics primarily distinguishes two types of variables: discrete and continuous. This distinction is fundamental for choosing the most appropriate data analysis techniques and visualisations.

Discrete variables

Discrete variables are those that take counted or distinct values. These data appear in separate units and are easily countable. Typical examples include the number of children in a family, the number of parked cars, or the number of sales completed in a day. Discrete variables are often represented through bar charts in Tableau, as these allow clear visualisation of the distinction between different units.
Which graphs to use with Tableau: a bar chart showing the number of sales per product. Each bar represents a distinct product, and the height of the bar indicates the total number of sales for that product. This type of visualisation helps to quickly identify which products are the most popular or those that need more attention.

Example with Tableau: the bar chart below shows the total sales for each product subcategory, which is discrete data: each bar represents a different subcategory, and the height of the bar indicates the total sales in that subcategory. This type of visualisation is particularly useful for easily comparing performance across different categories and for identifying which subcategories contribute most or least to overall revenue. It is immediately evident which subcategories are the best-selling and which are the least-selling, allowing analysts and decision-makers to identify areas of strength and improvement.

Continuous variables

Conversely, continuous variables can take any value within a continuous range. These data represent measurements and can be divided into increasingly smaller units, for example, time, temperature, or income. Unlike discrete variables, continuous variables offer a more fluid and detailed view of the phenomenon under examination.
Which graphs to use with Tableau: a line chart illustrating temperature variation over the course of a day. Each point on the chart represents the temperature measured at a specific moment, and the line connecting the points shows how it changes over time. This type of visualisation is ideal for observing trends and patterns over time.

Example with Tableau: the line chart below clearly shows total sales (represented on the Y-axis) in relation to months (represented on the X-axis), with each point indicating the total sales for each month. The line connecting the points makes it easy to follow sales fluctuations over time, highlighting trends, cycles, or seasonal patterns and demonstrates how sales vary month by month, offering an immediate view of any increases or decreases, which could be correlated with specific events, promotions, or market trends. This type of visualisation is extremely useful as it allows stakeholders and the decision-making team to quickly identify periods of greater and lesser performance, thus informing sales and marketing strategy.

Visualising discrete and continuous variables in Tableau
Tableau offers a range of powerful tools for visualising both discrete and continuous variables, enabling analysts to transform complex data into intuitive and informative charts. By using the different chart types available, it is possible to effectively explore and communicate the unique characteristics of each variable.

Tip: when working with Tableau, it is useful to experiment with different types of visualisations to discover which best communicates the information contained in your data. Remember to consider the audience for whom the analysis is intended and the objective of the analysis itself.

In conclusion, understanding the distinction between discrete and continuous variables is a crucial step for any data analysis. This knowledge guides the choice of the most suitable analysis techniques and visualisations, allowing analysts to extract and communicate valuable insights from their datasets. The next section will explore how key measures such as mean, variance, and standard deviation can be calculated and visually represented for both types of variables.

Measurements in datasets

In this section, we focus on how to summarise and interpret datasets through the use of fundamental statistical measures. Understanding these measures is vital for any Data Analyst, as they offer an immediate overview of the main characteristics of a dataset. Using Tableau, we can visualise these measures in ways that facilitate their interpretation.

Mean

The mean represents the average value of a set of numbers and is calculated by adding all the values and dividing the result by the total number of values. The mean is often used to identify the central location of data in a set, but it can be influenced by extremely high or low values (outliers).

Which graphs to use with Tableau: a bar chart with a horizontal line representing the mean of the values. This can be particularly useful for visualising how individual values are distributed relative to the overall mean.

Example with Tableau: the following bar chart shows the average sales for each subcategory within broader product categories. This type of chart is useful for comparing average sales across various levels of product detail and for revealing which subcategories have on average better or worse performance within the categories.

Variance and Standard Deviation

Variance measures how much the data spreads relative to the mean; in other words, it indicates how much the values in the dataset differ from each other. Standard deviation is the square root of variance and provides a measure of data dispersion in original units, making it simpler to interpret compared to variance.

Which graphs to use with Tableau: a histogram showing the distribution of data, with overlaid vertical lines to indicate the mean and standard deviation. This type of visualisation helps to understand the dispersion of data around the mean.

Example with Tableau: in the following chart, we have leveraged Tableau's analytical capabilities to create a "control chart", a quality tool used to monitor the stability and control of a process over time. A control chart is particularly useful in identifying anomalies and trends, allowing businesses to maintain efficient and predictable processes. The chart visualises an example of monthly sales with several key elements integrated:

• Time series: sales are represented in a time series to capture their evolution over time.
• Average sales: a reference line crosses the graph, showing the average monthly sales as a central reference point.
• Control limits: we have set the upper and lower control limits at a specific number of standard deviations from the mean (1-3). This defines the expected range of variation and identifies any given point that falls outside this range as a potentially important signal.
• Anomaly indicators: points representing monthly sales above or below these thresholds indicate unusual events. For example, months recording sales beyond three standard deviations from the mean are considered statistically improbable and might suggest the need for further investigation.
• The chart is interactive: users can modify the number of standard deviations for the control limits thanks to a parameter, which allows for a more or less conservative analysis. This offers a magnifying lens through which to examine fluctuations in sales: a parameter set at one standard deviation will highlight even minor fluctuations, while a parameter of three will provide a view of only the most drastic variations.

This chart not only serves as a diagnostic tool for identifying anomalies over time, but can also guide operational and strategic decisions, such as inventory management or sales performance analysis. Through Tableau, sales data transforms into a powerful storytelling tool that drives business action based on concrete and measurable insights.

How to Visualise Measures in Datasets with Tableau
Visualisations in Tableau can transform these abstract measures into intuitive graphical representations, making trends, patterns, and anomalies immediately evident.

• Mean: use line or bar charts to overlay the mean on the actual data. This helps to visualise the relationship between individual data points and the average value of the set.
• Variance and standard deviation: charts such as histograms or box plots are particularly effective for showing data dispersion. Standard deviation can be visualised as an interval around the mean, offering a clear visual representation of data variability.

Considerations on the use of measures in datasets
When analysing these indicators, it is important to remember that the mean and standard deviation can be influenced by outliers. In such cases, other measures of central tendency, such as the median, can provide a more faithful representation of the data distribution. Tableau allows you to easily explore these alternatives through different chart types and configurations, enabling analysts to choose the visualisation most suited to their specific analysis context.

In conclusion, understanding and visualising fundamental measures in datasets is essential for data analysis. Tableau offers the tools to represent these measures in ways that make statistical concepts accessible and immediately understandable, allowing analysts to extract valuable insights and communicate them effectively. The next section will explore data distributions, another key concept for interpreting and analysing datasets in depth.

Distributions

This section deals with how data is distributed across different values or categories, offering valuable insights into the nature of the phenomena studied. Understanding distributions is fundamental for data analysis, as it provides the basis for further statistical investigations, such as hypothesis testing and regression. Through Tableau, we can easily visualise these distributions, making the concepts more accessible and interpretable.

Frequency and Proportional Distributions

• Frequency distributions: show how data groups for different values or categories, counting the number of occurrences for each. This type of distribution is useful for identifying patterns, such as the prevalence of certain values or categories in the data.
• Proportional distributions: unlike frequency distributions that focus on counting, proportional distributions examine the percentage or proportion that each group represents in the total data. They are particularly useful for comparing groups of different sizes.

Which graphs to use with Tableau: create a pie chart or bar chart to visualise the proportions of different categories in a dataset, such as the distribution of sales by region. These charts allow you to quickly visualise which category dominates or is least represented in the dataset.

Example with Tableau: the histogram below visualises the frequency distribution of quantities of products sold, broken down by category. Each column, or 'bin', represents a range of quantities of products sold, while the height and colour of the columns reflect the count and proportion of sales within that bin. The histogram is a powerful visualisation tool for sales analysis: revealing not only the most frequently purchased quantities, but also allowing direct comparison between categories. For example, we can immediately observe that most "Office Supplies" transactions involve the purchase of small quantities, a valuable insight for optimising stock and marketing strategies. The proportions highlighted in the chart further emphasise the prevalence of these small transactions and can guide operational decisions such as inventory planning or customisation of promotions based on the most common purchase frequency. This type of analysis and visualisation can help businesses better understand their customers' behaviours and adjust their operational strategies accordingly.

Symmetric and Asymmetric Distributions

• Symmetric distributions: in a symmetric distribution, data is distributed equally around a central point, typically the mean. The graph of a symmetric distribution has the same appearance on both sides of the centre.
• Asymmetric distributions: distributions can be asymmetric, or "skewed", to the right (positively skewed) or to the left (negatively skewed). This indicates that one tail of the distribution is longer than the other, suggesting a group of outliers or a trend in the data that deviates from the norm.

Which graphs to use with Tableau: use a histogram to show whether a distribution is symmetric or asymmetric. Histograms offer an immediate visualisation of the shape of the distribution, making asymmetries evident.

Normal Distribution

• The normal distribution, or Gaussian distribution, is one of the most important distributions in statistics. Characterised by a symmetric bell shape, it describes how data tends to cluster around a mean, with variation decreasing as one moves away from the mean. Knowledge of the normal distribution is crucial, as many statistical techniques assume that data follows this distribution.

Which graphs to use with Tableau: create a bell curve to represent the normal distribution of data. This type of chart is effective for showing how most data concentrates around the mean and how data frequency decreases as distance from the mean increases.

Visualising distributions with Tableau
Tableau's ability to transform complex data into clear and interactive visualisations allows analysts to effectively explore and communicate the characteristics of data distributions. Experimenting with different chart types can help find the most suitable visualisation for the message you wish to convey, thus improving data understanding and interpretation.

Example with Tableau: the chart below reflects a detailed analysis of the profit distribution in the "Sample – Superstore" dataset. Using both a histogram and a density curve, we can precisely observe the nature of the distribution of data relating to profits and determine whether they show characteristics of symmetry and normality.

• Shape of the distribution: the symmetric figure of the histogram and the corresponding density curve are indicative of a symmetric distribution, where data is equally distributed on both sides of the mean. This balance is a hallmark of normal distributions, which are fundamental in statistics due to their properties and applications in hypothesis testing and statistical inference.
• The bell-shaped density curve: the density curve that emerges from the histogram has the characteristic shape of a bell, which suggests a normal distribution of profits. In a perfectly normal distribution, approximately 68% of the data would fall within one standard deviation from the mean, 95% within two standard deviations, and almost 99.7% within three standard deviations.
• Interpretation of asymmetric distributions: if the histogram had shown a longer tail on one side or the other, this would have indicated an asymmetric distribution, with data having a tendency to lean towards values higher or lower than the mean. Such distributions require particular attention, as statistical techniques for normal distributions might not be appropriate.

Our chart not only confirms that profits have a general tendency towards normality, but also that there are no indications of significant asymmetry that could indicate deviations from standard operational routine. This information can be vital for businesses seeking to establish financial forecasts, set performance benchmarks, or assess the probability of rare events.

In the next section, we will examine in detail how visualisations, such as histograms and box plots, can be used to analyse and interpret distributions, thereby offering further insight into the dynamics within the data.

Visualisations

Visualisations can transform abstract numbers into intuitive and easily interpretable charts. Visualisation is a crucial part of data analysis, as it allows the discovery of patterns, trends, and outliers that would not be immediately evident from examining raw numbers alone. Two of the most powerful tools at our disposal are the histogram and the box plot, each of which offers a unique way of representing data distributions.

Histograms

Histograms are used to show the distribution of data by grouping information into bins (intervals) and counting the number of observations in each bin. They are particularly useful for visualising the shape of the data distribution, such as whether the data is symmetric, skewed, or follows a normal distribution.
Which graphs to use with Tableau: by creating a histogram of monthly sales, you can quickly identify in which months there were peaks or drops in sales. By observing the shape of the histogram, you can make hypotheses about seasonal causes or events that influenced sales.

Box Plot

Box plots (or box-and-whisker diagrams) provide a visual summary of five main statistical measures: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. They offer a compact view of the data distribution, highlighting the presence of outliers and the symmetry of the distribution.
Which graphs to use with Tableau: A box plot can be used to analyse the distribution of sales prices of different products. This can quickly identify which products exhibit greater price variability and whether any outliers warrant further investigation.

How to Visualize Distributions with Tableau

Creating Histograms

1. Data Selection: choose the dataset to analyze.
2. Defining Bins: set the bins to reflect meaningful intervals for the analysis.
3. Visualization: drag the bin field to the X-axis and the data count to the Y-axis to create the histogram.

Creating Box Plots

• Data Selection: identify the variable of interest for analysis.
• Arrangement: Place the variable on the Y-axis and a categorical variable on the X-axis if you want to compare distributions across categories.
• Chart Choice: select the "Box Plot" option from Tableau to generate the diagram.

Example with Tableau (1): the following box plot focuses on the distribution of sales within product categories, offering an overview of how sales vary between different categories. It is useful for highlighting differences in sales patterns between categories, such as the "Technology" category which might have higher average sales but also greater variability. This visualisation can be particularly useful if we are trying to explain how different types of products perform in the market or if we are trying to analyse pricing or promotion strategies for specific categories. Furthermore, this visualisation is suitable in contexts more focused on product assortment aspects, category management, and pricing strategies, as it offers a clear representation of the distribution of sales across product categories, which is fundamental for inventory management and for the allocation of marketing resources.

Example with Tableau (2): the box plot below, on the other hand, shows the distribution of sales across different customer segments and highlights specific sales per customer, thus offering a view of customer purchasing behaviour based on their segment. This is particularly useful if we aim to discuss the personalisation of sales strategies or the importance of recognising and incentivising key customers in each segment. Furthermore, it provides a clear illustration of how some customers can have a significant impact on overall sales and could inspire strategies to engage with these individuals or businesses. Compared to the previous visualisation, focused on analysing product categories and managing business strategies, this is more oriented towards analysing customer behaviour and optimising customer relationships and value.

Using Visualizations for Analysis

Visualisations help not only to understand the data available, but also to communicate it effectively to an audience. Histograms and box plots, in particular, are essential tools in a data analyst's arsenal for illustrating the key characteristics of a dataset. Through the use of Tableau, it is possible to customise these visualisations to suit the specific needs of the analysis, making the results accessible even to those without advanced statistical training.

In the next section, we will elaborate on the concept of hypothesis testing and how visualisations can support the interpretation of test results, providing deeper insights into the analysed data.

Hypothesis testing

Hypothesis testing plays a crucial role in statistical analysis, enabling analysts to evaluate claims or theories about data. This process uses sample data to test whether a certain hypothesis about the population from which the sample was drawn is likely or not. Through the use of Tableau, we can visualise the results of hypothesis tests in a way that is understandable even to those without advanced statistical training.

Fundamental Concepts

• Null hypothesis (H0): the null hypothesis assumes that there is no significant difference or relationship between the groups or variables being examined. It is the hypothesis that the test seeks to refute.
• Alternative hypothesis (H1): the alternative hypothesis proposes a significant difference or relationship between the groups or variables. It is what one hopes to demonstrate through the test.
• P-value: the p-value indicates the probability of obtaining the observed results, or more extreme results, assuming that the null hypothesis is true. A low p-value (typically less than 0.05) suggests that it is unlikely to observe such data by chance, thus leading to rejection of the null hypothesis.
• Confidence and Confidence Interval: the confidence interval provides a range within which we expect the true population value to lie, with a certain level of confidence (often 95%).

Visualising Hypothesis Tests in Tableau

While Tableau does not directly perform hypothesis testing as statistical packages do, it can be used to visualise data so that decisions made through hypothesis testing are clear and grounded in visual evidence.

• Scatter plots: can be used to show the relationships between two variables, helping to identify patterns that support or refute the alternative hypothesis.
• Box plots: useful for comparing distributions of a variable across different groups, box plots can highlight significant differences in medians, supporting rejection of the null hypothesis.
• Bar and Line Charts: to show significant differences in terms of mean or proportions between groups, which can indicate whether the alternative hypothesis has a statistical basis.

Interpreting Results

The key to interpreting hypothesis test results is understanding that we are working with probabilities. Rejecting the null hypothesis does not definitively prove the alternative hypothesis, but indicates that the collected data are unlikely if the null hypothesis were true. Using visualisations in Tableau can help communicate these concepts, making hypothesis test results more intuitive and less abstract.

Considerations

Hypothesis testing is a fundamental component of statistical analysis, providing a framework for making data-driven decisions. Visualising results with Tableau not only helps interpret the data, but also facilitates sharing these results with a wider audience, making data analysis a more collaborative and inclusive process. Remember, the ultimate goal is to use data to make informed statements and take decisions based on concrete evidence.

Example with Tableau

The following scatter plot illustrates the relationship between average discounts applied and average profits obtained from products in the "Sample-Superstore" dataset. Through a linear regression model, we can predict the average impact of discounts on profits.

The regression line formula is as follows: Expected Profit = (Intercept) + (Slope) x (Average Discount), where "Intercept" represents the profit value when the discount is zero, and "Slope" indicates the change in expected profit for each unit change in discount.
For example, with the value "38.91″ for the intercept and "-133.86″ for the slope obtained from the regression model, to calculate the expected profit with an average discount of 10% we insert 0.1 (10% expressed as a decimal) into the equation: 38.91 + (-133.86 x 0.1) = 38.91 – 13.39 = 25.52. Therefore, if the average discount applied is 10%, the model predicts that the average profit would be $25.52. This analysis allows for a better understanding of how profits vary as discounts applied change and can help businesses optimise pricing strategies to maximise profitability.

Note: in the context of linear regression, it is important to verify that the slope and intercept are correctly indicated in the chart or in the analysis software report. The slope coefficient indicates how much the average profit is expected to change with a one percentage point change in average discount. A negative value for the slope (-133.86) indicates that there is a negative relationship between discount and profit, i.e. as the average discount increases, the average profit is expected to decrease. The very low p-value (0.0005003) suggests that the relationship between average discount and average profit is statistically significant, at least within the data sample represented in the chart.

Conclusion

Concluding our journey through the foundations of statistics and the power of data visualisation with Tableau, it is essential to reflect on the importance of these tools and concepts in data analysis. The ability to understand and apply statistical principles, together with the effective use of visualisation tools such as Tableau, not only significantly improves our ability to interpret data, but also opens the door to more informed decisions and deeper insights.

Statistics is much more than a set of numbers and calculations; it is the language through which data speak to us. Through the use of measures in datasets, understanding distributions and applying hypothesis tests, we are able to extract meaningful insights from large data sets, revealing the hidden stories behind the numbers. However, the real magic happens when we combine these analyses with the power of data visualisation offered by tools such as Tableau. This not only makes analysis results accessible to a wider audience, but also facilitates the discovery of patterns, trends and anomalies that might otherwise remain hidden.

Histograms, box plots and other visualisations become windows through which we can observe the world of data in new and illuminating ways. These tools allow us to present our results in a way that is immediately understandable, regardless of the audience's technical background. The ability to communicate analysis results effectively is just as important as the analysis itself, and data visualisation plays a key role in this process.

Ultimately, integrating statistics and data visualisation into our analytical toolkit not only enriches our understanding of data, but also improves our ability to make decisions based on it. Whether optimising business strategies, guiding public policy or advancing scientific research, data analysis supported by a solid understanding of statistics and enriched by effective visualisations is indispensable.

Next Steps

While this article provides an introduction to the fundamental principles of statistics and data visualisation with Tableau, there are many other techniques and tools to explore. I invite you to further practical experimentation, trying different types of data and visualisations and applying these concepts to new and diverse analytical challenges. Remember: every dataset has a story to tell and with the right tools you can be the one to tell it.

Thank you for sharing this brief introductory journey into statistical analysis with Tableau. I hope you now feel more "equipped" to explore the vast and dynamic world of data, armed with statistics and Tableau. Happy analysing!

Note (1): the dashboard with the examples mentioned in the article is available on my personal Tableau Public page.

Note (2): Various articles will soon be available on the Blog that will cover these topics separately and in greater detail, including a tutorial on using and interpreting scatter plots in Tableau.

FAQ

The FAQ section aims to answer some of the most common questions regarding statistical analysis and the use of Tableau for data visualisation. These questions can help readers clarify doubts and further deepen their understanding of the concepts covered in the article.

These FAQs provide a starting point for further exploring data analysis and the use of Tableau. Continuing to ask questions and experiment with data is essential for developing a solid understanding of statistical analysis and data visualisation.

If you enjoyed the article and wish to delve deeper into these topics or simply connect to exchange ideas, feel free to visit my LinkedIn profile and connect with me. I look forward to hearing from you!