As Marie Davidian and Thomas A. Louis said:
"Statistics is the science of learning from data, and of measuring, controlling, and communicating uncertainty; and it thereby provides the navigation essential for controlling the course of scientific and societal advances" (DOI: 10.1126/science.1218685)
So we need statistics to make good or better decisions for problems that do not refer to individual cases, but on populations or mass phenomena or of which entire populations are affected.
Today statistics are part of our everyday life. Whenever you hear about proportions, averages, ranges and so on, there must be a statistic behind the numbers.
Basically we distinguish between descriptive statistics and inferential statistics:
Descriptive statistics
Descriptive statistics means the analysis of data that helps describe, show or summarize data in a meaningful way. Descriptive statistics do not allow us to make conclusions beyond the data we have analysed. They are simply a description of our data.Descriptive statistics is important because it allows us to summarize and visualize the data we have collected. By using tables and plots we get insight in patterns that emerge from our data. Descriptive statistics are used to inform us about the distributions of what we have measured or observed. Imagine you are a teacher and you have administered a math exam to your class. You may not only be interested on how each student of your class has performed but you may be interested in the overall perfomance of the students. You may want to know if the exam was difficult or easy. Maybe you even want to compare the exam to former exams. Descriptive statistics allow us to do this.
Inferential statistics
Until now it was all about our sample. Descriptive statistics is good for describing the data from our sample. But if we want to go further and make conclusions from our sample data to the population, we will need inferential statistics. Descriptive statistics are often reported together with a degree of accuracy, indicating the statistic’s value as an estimate of the real-world measure. For example the mean of a sample is the best estimator for the mean of the population the sample was drawn from. If we report only the mean of our sample we literally don't care about the mean of the population. We may, however, calculate an intervall around our mean that indicates the the range where the true population mean lies with a given certainty.Or, according to the example above you may want to know if the difference between the performance of the actual class compared to last year class' performance is significant, or if this difference occurred only by chance.
In general, inferential statistics are techniques that allow us to use samples in order to make generalizations about the populations from which the samples were drawn. There are two main goals of inferential statistics: 1) to estimate parameters in the population and 2) to test statistical hypotheses.
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| Descriptive and inferential statistics summarized |
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