Definition of Statistics

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.

Statistics vs Parameters:

• Statistics:
  • A collection of data, numbers, and non-numbers arranged in tables and or diagrams that describe or describe a problem
    • Population Statistics, births, education, production, agriculture, etc.
  • Size as representative of the data set
    • Mean, median, mode, standard deviation, variance, percent, etc.
• Parameters : the meaning is almost the same as statistics, the difference only lies in the data source used. Statistics use data sources that come from samples, while parameters use data sources that come from populations.
• Statistics are used to estimate the value of the population parameter.

Statistical Method

Statistical methods are the procedures used in collecting, presenting, analyzing, and interpreting data.

Scope of Statistics

Based on the orientation of the discussion:

• Mathematical statistics: theoretical statistics that are more oriented to understanding theoretical mathematical models and statistical techniques.
• Applied statistics: statistics that are more oriented towards an intuitive understanding of statistical concepts and techniques and their use in various fields

Based on the stages and objectives of the analysis:

• Descriptive statistics :
  • Descriptive statistics is concerned with the application of statistical methods regarding the collection, processing, and presentation of a data set so that it can provide useful information.
  • Statistics that use data in a group to explain or draw conclusions about that group only
  • Explain/describe various characteristics of data through:
    • Location Measures ( Central Tendency ): mode, mean, median, etc.
    • Measures of Variability/Dispersion: variance, standard deviation, range, etc.
    • Shape Size: skewness, kurtosis, box plot
    • Presentation of tables and graphs, for example
      • Frequency Distribution
      • Histogram, Pie chart, Box-Plot, etc.
• Inferential Statistics :
  • Inference statistics is a branch of statistical science that deals with the application of statistical methods to estimate and/or test the hypothesized population characteristics based on sample data.
  • Statistics that use data from a sample to draw conclusions about the population from which the sample was drawn
  • Making various inferences (drawing conclusions) on a set of data originating from a sample. The inference actions such as making estimates, forecasting, decision making and so on.

The purpose of statistics is basically to describe the sample data, then make inferences to the data population based on the information (descriptive statistical results) contained in the sample. Thus, in practice the two parts of statistics are used together, generally starting with descriptive statistics and then continuing with various statistical analyzes for inference .

Based on the distribution assumptions used:

• Statistics are parametric :
  • statistical measurement techniques based on certain assumptions, for example data taken from a normally distributed population.
  • This statistical technique is used for data with interval and ratio scales .
• Non-parametric statistics :
  • statistical techniques that use few (or even no) assumptions are sometimes also known as statistical models that are independent of certain distributions.
  • This non parametric statistic is used to analyze nominal and ordinal scale data .
• In general, every data testing technique with parametric statistical techniques has its equivalent technique in non-parametric statistics. The equivalent technique in non-parametric statistics is usually used if the interval/ratio data does not meet certain assumptions, for example the data is not normally distributed. For example, if the data to be analyzed using the F-Test (Anova) does not meet the ANOVA assumptions (additive, normality, homoscedasticity, independence) even though the transformation has been carried out, then the last alternative we can test it using the Kruskal-Wallis test (One Way Anova - RAL) or Friedman Test (RAK) which is a nonparametric statistical technique.

Based on the number of variables:

• Univariate Statistics : statistical analysis technique that only involves one dependent variable
• Multivariate Statistics : statistical analysis technique that involves more than one dependent variable at once.<

The role of statistics in research

• Provides information about the distribution characteristics of a particular population, both discrete and continuous. This knowledge is useful in understanding the behavior of the population being observed
• Provide practical procedures in conducting data collection surveys through data collection methods (sampling techniques). This knowledge is useful for obtaining reliable measurement results
• Provide practical procedures for predicting the characteristics of a population through a sample characteristics approach, either through the estimation method, hypothesis testing method, and variance analysis method. This knowledge is useful for knowing the size of the concentration and the size of the spread as well as the differences and similarities of the population.
• Provides a practical procedure for predicting the state of a particular object in the future based on past and present conditions. Through the regression method and the time series method. This knowledge is useful in reducing the risk due to uncertainty faced in the future.
• Provide practical procedures for testing qualitative data through non-parametric statistics.

Relationship between statistics and research methods

Statistics is one of the main components in the stages of research methods, determining sample size, collecting, presenting, and analyzing data and to see its scientific degree.