Chapter 1 Introduction
1.1 What is Statistics?
Statistics is a collection of methods for collecting, organising and analyzing data, interpreting data and drawing conclusions from and visualising data (Witte R. S. and Witte J. S. 2017). Statistical knowledge helps us to determine the best methods to collect data and to employ appropriate analyses and effectively present and communicate the results. Statistical practices should begin long before the analysis phase to avoid problems with the data collected, like biased samples and over generalisation (Frost J. 2019).
There are two main branches of statistics: descriptive statistics and inferential statistics.
1.1.1 Descriptive Statistics
A descriptive statistic is a summary statistic that is used to describe or summarise data while descriptive statistics is the process of using those statistics to describe the characteristics of a sample or a population (Witte R. S. and Witte J. S. 2017). Descriptive statistics may describe a data set but they do not attempt to generalise beyond the set of observations or measurements made from the data set (Frost J. 2019).
The distributions detailing the frequencies of values, measures of central tendency such as (mean, median and the mode) and measures of dispersion (range, interquartile range and standard deviation) are the most important tools. Descriptive statistics can also be used to describe the data set in terms of skew and correlation.
1.1.2 Inferential Statistics
Inferential statistical is used to make inferences about the properties of a population (Witte R. S. and Witte J. S. 2017). Sometimes these inferences are referred to as predictions. Inferential statistics involves hypothesis testing, confidence intervals and regression analysis. Since the goal is to take a sample and generalise its properties to a population we need to have confidence that the sample accurately reflects the population. We must ensure that the population is well defined, that we draw a representative sample from that population and that we use analyses that incorporate the sampling error (Frost J. 2019).
Random sampling is the primary method used for obtaining samples that reflect the population however it can often be difficult to obtain a random sample.
Summary
There are two main branches of statistics: descriptive statistics and inferential statistics.
Descriptive statistics describes the characteristics of a sample or a population using measures of central tendency and measures of dispersion.
Inferential statistics is used to make inferences about the properties of a population.