Читать книгу End-to-end Data Analytics for Product Development - Chris Jones - Страница 25

After describing important characteristics of sample data through descriptive statistics, the second step of a statistical analysis is usually inferential analysis, where sample findings are generalized to the referring population.

Inferential techniques use descriptive statistics such as:

sample mean “ ”

sample proportion “p”

sample standard deviation “S”

to draw conclusions about the corresponding unknown quantities of the population, called parameters:

population mean: “μ”

population proportion “π”

population standard deviation “σ”

Note that it is standard to use Greek letters for certain parameters, such as μ to stand for a population mean, σ for a population standard deviation, σ² for a population variance, and π for a proportion of statistical units having a characteristic of interest.

A statistic (mean, proportion, variance) describes a characteristic of the sample (central tendency, variability, shape of data) and is known.

A parameter (mean, proportion, variance) describes a characteristic of the population (central tendency, variability, shape of data) and is unknown.

Statistical inference uses sample data to draw conclusions about a population with a known level of risk. In general, statistical inference proceeds as follows:

1 We are interested in a population.

2 We identify parameters of that population that will help us understand it better.

3 We take a random sample and compute sample statistics.

4 Through inferential techniques, we use the sample statistics to infer facts about the population parameters of interest.