Statistics for Strategic Decision-Making and Analysis

The Role of Statistics in Information Analysis

As Mintzberg described in 1987, a strategy can be defined as a plan of action that requires decision-making, based on the efficient use of available resources. It is essential that these plans of action are based on reliable knowledge provided by sound data analysis. Today, we live in a flood of data that must be efficiently harnessed for decision-making. The way to transform data into valuable knowledge for decision-making is based on the techniques and methods provided by Statistics.

Statistics is the science that deals with the collection, organization, presentation, analysis, and interpretation of numerical data in order to make more effective decisions.

Defining Statistics and Its Core Steps

The three fundamental steps of statistics are:

• Statistical steps: Data collection, analysis, and interpretation.

Branches of Statistics

Statistics is the basis for information analysis and decision-making. Generally, the study of statistics is divided into two categories: descriptive statistics and inferential statistics (or statistical inference).

• Branches of statistics: Descriptive and inferential.

In an organization, a large amount of data and information is produced that must be transformed so that actions can be generated from the knowledge created.

Stages of Statistical Investigation

The steps followed to carry out an entire statistical process are known as statistical investigation and include the following stages:

• Selection and determination of the population or sample.
• Obtaining data through direct observation of elements, conducting surveys and interviews, and carrying out experiments.
• Classification, tabulation, and organization of data.
• Descriptive analysis of data, obtaining statistical indicators such as measures of central tendency, dispersion, position, and shape.
• Inferential analysis of data: Techniques involving probabilistic elements are applied, enabling conclusions to be inferred from a sample to the population.

Business Applications of Statistical Analysis

The use of statistics in business is extensive, for example:

• In Accounting: Analysis of key ratios and metrics, inventory management, etc.
• In Finance: Analysis of the behavior of key performance variables (KPI or Key Performance Indicator) such as profitability, sales, capital levels, share value, etc.
• In Marketing: To determine the best customers, calculate their value to the business, understand customer attrition levels, identify profiles of the best customers, etc.
• In Production: To measure quality levels, compliance with standards, value chain analysis, etc.
• In Economics: To analyze the behavior of macroeconomic variables such as inflation, exchange rates, unemployment, etc. In microeconomics, the analysis of variables such as supply, demand, price, resource allocation, etc.

Understanding Population and Sample

In the definition of inferential statistics, reference is made to the terms population and sample.

In statistics, a population is the set of individuals or elements of interest in a study. A population can consist of individuals, objects, or measures of interest. From a statistical perspective, a population does not always have to relate to people. To infer something about a population, it is common to take a sample from it.

A sample is a subset or part of the population of interest. In most cases, conducting a study on all elements of a population is too costly, time-consuming, requires a prohibitive amount of resources, or is virtually impossible. In the vast majority of cases, it is not necessary to do so.

For the sample to be representative of the population from which it is drawn, it must be random, meaning that all elements had the same chance of being selected. This way, inferences can be made about the characteristics of a population from the results obtained from a sample.

Graph indicating that a sample is part of a population and the selection process is called sampling.

Types of Data and Measurement Scales

Variables and Data

Variables are a defined set of characteristics of the elements of a population, which can take on or be assigned different values. There are two types of variables:

• Qualitative: These represent a quality, category, attribute, or non-numeric characteristic of the elements of a population or sample. Some examples of qualitative variables are: marital status, eye color, gender, clothing brand, etc. As expected, the values that can be assigned to these variables are not numerical, or if they are, these values represent a coding (e.g., 0=single, 1=married) and the numerical operations performed between them are meaningless.
• Quantitative: Unlike qualitative variables, quantitative variables represent characteristics that are invariably expressed through quantities or numerical measures. The measured or quantified value is inherent to the object and does not depend on the observer.

Classification of Quantitative Variables

Quantitative variables are further classified into two types:

• Discrete: These take on only certain values, and there is no continuity between one and another. In other words, discrete quantitative variables take values that can be counted. For example, the number of family members, the number of cars a person owns, the number of defective parts, the number of branches, the score assigned to a multiple-choice exam question (which can be a fraction), etc.
• Continuous: These can take continuous values within a specific interval. In general, the values of a continuous quantitative variable can be measured using an appropriate scale. Some examples are: temperature, volume, family income, weight, waiting time, etc.

When information is collected from all the elements of a sample or a population, a set of data is obtained. In other words, data are the different values collected for a variable. It is important to note that data are quantitative or qualitative values of a variable obtained as a result of sampling a population. When information is collected from all the elements of a sample or a population, a data set is obtained.

For example, if a study is required on the characteristics of cars sold in a city, where the variables of interest are color, length, and height, the data assigned to these variables for a sample element would be C= green, L=4.57 meters, and A=1.74 meters. This same information should be collected for the rest of the sample elements to obtain a data set (database).

Levels of Measurement Scales

As mentioned earlier, there are data that represent different characteristics of variables, so not all can be treated the same when summarizing and presenting information. Therefore, it is important to know the different measurement scales.

Nominal Level Data

This is the most basic level and is used only for qualitative variables; its use is limited to classification and counting. There is no pre-established ordering of the values that the variable can take.

Example: The variable gender has two possible values: male and female; these two labels have no fixed order and only the number of data corresponding to each can be determined.

Ordinal Level Data

This level also corresponds to qualitative variables, but those in which values must respect an ordering.

Example: The variable customer service can have values such as excellent, good, average, poor, and very poor, in that order. In this case, receiving a rating of excellent has a relatively higher value than a rating of good, and this a relatively higher value than the rating of average, and so on.

Interval Level Data

At this level, ordinal level characteristics apply and, in addition, the difference between one value and another is constant. At this level, the value of zero does not imply the absence of the characteristic.

Example: If one room has a temperature of 30 degrees Celsius and another 32, the difference (2 degrees) is the same as between two rooms with 26 and 28 degrees respectively. The unit of measure on this scale is constant (1 degree Celsius); however, if you divide 32/30, the obtained value is not the same as if you divide 28/26. Furthermore, the value of zero degrees is just another value, and it does not represent the absence of temperature.

Ratio Level Data

This is the highest level and provides the most information about quantitative data. It meets the characteristics of the interval level and, furthermore, the value of zero represents the total absence of the characteristic, and the division between two values (ratio) has meaningful significance.

Example: The variable salary implies that zero represents the total absence of money, and the difference between two salaries of $4,000 and $4,500 is the same difference as between two salaries of $5,000 and $5,500.