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Statistics

A collection of articles on descriptive and inferential statistics: Basic Statistics ( Definition of Statistics, Population and Sample, Variables and Data, Variable Measurement Scale ); Descriptive Statistics ( Definition of Descriptive Statistics, Size of Data Concentration, Size of Spread, Examples of Skewness and Kurtosis Calculations, Frequency Distribution ); Data Exploration ( Explorative data analysis, Stemplot, Knowing Box-Plot ); Correlation and Regression; Student 's t-test ( student t-test, 2-population t-test with homogeneous variance, 2-student t-test with heterogeneous variance, Paired t-test ); and some Non-Parametric tests (McNemar test, Wilcoxon test for paired data )

Statistics is a branch of applied mathematics which consists of theories and methods on how to collect, measure, classify, calculate, explain, synthesize, analyze, and interpret data obtained systematically. Thus, it consists of a set of procedures on how to:

  • Collecting data
  • Summarizing data
  • Processing data
  • Presenting data
  • Draw conclusions and interpret data based on data collection and analysis results

This article will briefly describe the meaning and differences of statistics vs. parameters , statistical methods, descriptive statistics vs. inferential statistics , mathematical statistics vs. applied statistics , parametric vs. non-parametric statistics , and univariate and multivariate statistics and the role of statistics in research.

Variable measurement is the process of assigning values or attributes to an object. There are four types of Variable Measurement Scale, namely Nominal, Ordinal, Interval, Ratio. The lowest scale is the Nominal and the highest is the Ratio Scale. A measurement scale that is higher will have the characteristics of a measurement scale below it. The four measurement scales were proposed by a psychologist, Stanley Smith Stevens, in 1946 in one of his scientific articles entitled "On the theory of scales of measurement".

The focus of research design and statistical analysis is the study of variables. When you want to study a phenomenon, the first step is to define the phenomenon under study, in this case is to determine the variables that we observe and then determine how you measure these variables. This process is known as operational definition . It is clear here that to understand a phenomenon, we must first understand the terms variables and measurement scales. If you do not clearly define how to measure the variables you want to study, you will eventually experience confusion in determining the right research design and in determining the appropriate statistical analysis procedure.

The population is the whole of the research object which is the center of attention and is the source of research data. The object of research can be humans, animals, plants, symptoms, values, events, attitudes to life, and so on. The sample is part of the population selected by using certain rules, which are used to collect information/data that describes the nature or characteristics of the population.

If we look at the definition, the definition of population can be very diverse, so we must define the population clearly and precisely. On the other hand, a sample that is representative of the population must be able to describe the characteristics of the population because the sample is used to generalize a population. Thus, the sample must be truly representative so that it can represent and reflect the characteristics of the population from which the sample was taken.

Statistics is a set of procedures for collecting, measuring, classifying, calculating, explaining, synthesizing, analyzing, and interpreting quantitative data obtained systematically. Broadly speaking, statistics are divided into two main components, namely descriptive statistics and inferential statistics . Descriptive statistics use numerical and graphical procedures to summarize data sets in a clear and understandable way, while inferential statistics provide procedures for drawing conclusions about the population based on the sample we observe. Descriptive statistics helps us to simplify large amounts of data in a logical way. Data that is much reduced and summarized so that it is simpler and easier to interpret.

Variable comes from the words " vary " and " able " which means " change " and " can". So, literally means variable is mutable , so each variable can be assigned a value and that value is arbitrary. The value can be quantitative (measured and/or calculated, can be expressed with numbers) can also be qualitative (the number and degree of attributes expressed by quality values). Variables are important elements in research problems. In statistics, variables are defined as concepts, qualities, characteristics, attributes, or properties of an object (people, objects, places, etc.) whose values vary from one object to another and have been determined by researchers to be studied and conclusions drawn . Characteristics are certain characteristics of the object we are examining, which can distinguish the object from other objects, while the object whose characteristics we are observing is called the unit of observation and a certain number or category (quality value) of an object that we are observing is called variate (value). The collection of values obtained from the measurement or calculation of a variable is called data .

One of the most important aspects to describe the distribution of data is the value of the observation data center (Central Tendency). Any arithmetic measurement that is intended to describe a value that represents the central value or central value of a data set (set of observations) is known as a measure of data centering (central tendency). There are three commonly used data concentration measures, namely:

  • Mean (Average arithmetic/arithmetic average)
  • Median
  • Mode
  • Geometric Mean
  • Harmonic Mean

In this article, we will discuss the meaning of several measures of data concentration accompanied by examples of calculations, both for single data or data that have been grouped in a frequency distribution table. In addition to the statistical measures above, several other statistical measures will be discussed, such as the Geometric Mean , Harmonic Average ( H) as well as some important characteristics that need to be understood for a good measure of central tendency and how to choose or use the exact value of central tendency.