Despite plenty of evidence for the “cognitive biases” from which all decision-makers suffer, an astounding number of managerial decisions is still based on gut feelings rather than solid analysis. Among the many reasons for this may be a certain level of apprehension about the complexity of quantitative analysis and the methods it entails.
We believe that quantitative analysis should not remain the elusive domain of certain managerial disciplines that naturally revolve around numbers (e.g. finance) nor of a secretive clan of “geeks” who huddle over spreadsheets all day long. On the contrary, basic principles of quantitative analysis should be part of the toolbox of every manager. We make it a point to include them in our curriculum and to teach them in a non-threatening way that focuses on application rather than abstract statistical theory. Let’s take a look at some basic concepts….
Descriptive statistics – a number may say more than a thousand words
The starting point for quantitative analysis is often very simple. It begins with what we call “descriptive” statistics. The most popular descriptive statistic is the mean, with which everyone should be well familiar. However, when data have a substantial number of extreme values (which statisticians call “outliers”) then the median might give a better idea of where the “middle” of the data is located. For example, when official statistics report on salaries or household incomes for a particular job, profession or country, they will often refer to “median salaries” or “median household income”, which is an effective way of neutralizing the disproportional influence of extreme salaries or incomes.
In addition, it may be useful to master some basic statistics that indicate how much variability is in your data. The so-called “standard deviation” is the most popular measure in this respect. Computing these statistics, for instance in Excel, is child’s play, and if you master them, you can describe the shape of your data with only one or two numbers that will tell a good story.
Inferential statistics – how to learn from (relatively) small samples about (potentially very) large populations
While “descriptive” statistics are an interesting starting point, the type of statistics that we label as “inferential” are infinitely more powerful. The basic intuition behind them is straightforward. Let’s assume that you would like to know something about a very large population, for instance, how much the citizens of a particular country spend on average on their vacations every year. Gaining precise information about this “population mean” will be impossible for purely practical reasons. You will never have the time and the resources to collect these data for every single person or household in a given country. This is where inferential statistics come into play. They allow you to use data from a relatively small “sample” (often not more than a couple of hundred observations) to draw astonishingly precise conclusions about the general population behind this sample. The appeal of this approach should be intuitively clear to every manager as the process saves both time and money. There is a great number of techniques that can be subsumed under the umbrella of “inferential statistics”. Below I will outline some basic applications.
Confidence intervals
Very often we would like to know something about a mean in a population (for instance, the average spending on fast food per year) or about a proportion in a population (for instance, the proportion of individuals who consider buying an electric vehicle or voting for a political candidate). In this case we could, of course, simply compute the mean or the proportion in our sample and take this as the best bet for the population. There is a more sophisticated method, however, and that is the confidence interval. A confidence interval allows us to say that with a particular probability (frequently we choose 95%) the value for the mean or the proportion will lie in a specific range. With relatively small samples the range we can determine will often be remarkably narrow and precise. The advantage of the confidence interval is that in addition to giving an indication of where the population mean or proportion should lie, we also indicate how much uncertainty surrounds our estimate.
Tests for differences in means and proportions
Another practical problem we often face is that we would like to know whether means or proportions are different across two or more populations. To take a practical example, we might be asking ourselves whether the average salaries for a given position differ between company A and company B. Or we might wonder whether passengers’ average assessment of cabin comfort differs across five different types of aircraft. In all of these situations, we can use samples to run statistical tests which will allow us to determine whether there is what we call a “significant” difference between the populations we are looking at. Again, once you understand how to interpret the results of these tests, which in and by itself is not overly complicated, running them on programs like Excel or more advanced software for statistical analysis is very simple and not time-consuming at all.
Exploring relationships with correlational techniques
Last but not least, the potentially most interesting questions that we can ask ourselves concern the issue of whether two or more variables are related to each other. For instance, is a particular leadership style related to higher employee performance? Is affiliation with a chain related to operating performance? Or is proactive service behavior related to guest satisfaction? Questions of these types can be tackled with so-called “correlational” techniques, including correlation and regression analysis, allowing for really interesting and practically relevant insights.
Conclusion
Beyond the methods outlined above, research methods specialists have obviously developed an almost unlimited array of more complex methods for more and more complex problems. But we at EHL believe that the key point here is not to turn you into “stats nerds”. In a world where apprehension about quantitative methods is widespread, the good news is that mastery of a small number of basic techniques can quickly propel you to the top of the heap and give you a competitive advantage. And even if you do not apply these methods in your daily lives, understanding them may help you decode numerical results that are communicated to you, ask informed questions and develop a feeling for numbers that are reliable vs. those that have been “tortured”.
