Key statistical terms explained | Tangente

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Statistics is the branch of applied mathematics concerned with quantitative data. It studies individuals, the basic units of observation or measurement. All the individuals studied make up a population.

A statistical variable is a characteristic shared by every individual in a population but whose value may differ from one individual to another. We generally distinguish between qualitative variables, whose values are discrete categories ("blue", "very satisfied", "yes"…), and quantitative variables, whose values are discrete or continuous quantities.

Descriptive statistics aims to summarize the values taken by variables within a given population, using suitable graphs or measures. The most common statistical measures include:

• For qualitative variables: the count and frequency (as a percentage) of each category within the population;

• For quantitative variables: the mean and median are measures of location for a statistical data set. The range, variance, and standard deviation are measures of dispersion.

A little terminology… ----------------------

The mean of a statistical data set is the sum of the data values divided by their number. Let x be the variable and x₁ to *x_n be its n possible values. The mean m* then satisfies $m=\frac{1}{n}{\sum }_{i=1}^n{x}_i\mathrm{.}m=\backslash frac\{1\}\{n\}\backslash sum\_\{i=1\}^\{n\}x\_i\backslash ,\; .$

The median of a statistical data set is the value that divides the data, arranged from smallest to largest, into two groups containing equal numbers of observations.

The variance of a statistical data set is the mean of the squared deviations from the mean. In other words: $\mathrm{V}\mathrm{a}\mathrm{r}=\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{x}}_{\mathrm{i}}-\mathrm{m}{)}^2\mathrm{.}\backslash rm\{Var\}=\backslash frac\{1\}\{n\}\backslash sum\_\{i=1\}^\{n\}(x\_i-m)^2\backslash ,\; .$

The standard deviation of a statistical data set is the square root of its variance. It is expressed in the same units as the variable.

The field of inferential statistics ------------------------------------------

Inferential statistics uses random samples to draw inferences about a variable in an entire population from its values in a sample. It encompasses surveys and estimation, as well as hypothesis testing.

Statistical modeling uses known data to build a mathematical model: a function that models the values of one variable (called the target variable, or response variable) from the values of other variables (the predictor variables, or explanatory variables) for the same individuals. Once specified, the statistical model can be used to make predictions from new values of the explanatory variables.

A hypothesis test is used to determine whether results obtained from a random sample are compatible with the null hypothesis, H₀, about the statistical distribution of a variable in a population. We calculate the probability of obtaining the observed result—for example, the observed mean when testing whether a mean has a specified value—assuming that H₀ is true. If this probability is considered "too low", we reject H₀.