In the process of conducting a research or working with a collection of information, a researcher during the first steps must organize and summarize the data meaningfully.
Descriptive statistics will now be a part of the researcher’s work as a set of methods used to collect, summarize, classify, and describe numerical facts in statistical analysis and to describe research data and information.
Descriptive statistics provide information, for example, about respondents’ “income“ or indicate whether education level influences the voting pattern of the sample. But we generally do not seek to know the attitudes and characteristics of, for example, 3,000 member samples in descriptive statistics; rather, we seek to actually create a description. In simple terms, “descriptive statistics intend to describe large amounts of data with graphs and summary tables, but do not draw conclusions about the population sampled“.
Because charts and tables are the main components, descriptive statistics make it easier to understand and visualize raw data, and in general, descriptive statistics reveal hidden points in the data and explore the data.
This operation has three general methods in descriptive statistics:
1- Statistical tables
2- Using statistical charts
3- Calculation of specific values
By creating a frequency distribution table, a large volume of irregular data can be easily displayed. The reason for creating a statistical table of frequency distribution is to organize data or observations into classes with the frequency of each class. In creating a frequency distribution table, special formulas are used to calculate the volume, amplitude of changes, and number of classes. In the frequency distribution statistical table, titles called absolute data frequency are used to know the number of data in each category, relative frequency, cumulative frequency, and relative cumulative frequency.
Creating a frequency distribution table is an economical and easy way to display large amounts of irregular data. But in classification, some information may be lost due to grouping error and ultimately affect the calculation of central indicators of statistical analysis. But the amount is often small and does not cause major problems.
Statistical chart in descriptive statistics is a suitable tool for visual representation of information. There are different types of statistical charts; these include histograms, bar graphs or bar charts, polygon charts, pie charts, or term clocks, time series charts, and distribution charts.
An important issue in statistical calculations is to determine the characteristics and general position of the data or the focus of the data; this is called calculating central indicators. If the central indicators are easy to calculate and it is possible to use all the data, it is also possible to calculate them in mathematical form; it can be said that the index is valid and valuable.
Three types of central indicators to calculate:
1- Mode: This index is used in research that the measurement criterion is nominal and to find a number with high repetition and to know the central tendencies in the fastest time.
2- Median: Median is also used as a view for nominal and ranking information.
3- Mean: Used to find a medium value and in research where the scale of data measurement is the minimum distance.
Dispersion indices are the distribution of each variable around the mean and focal point. Simply put, they show the researcher the extent of variation and dispersion among research data.Among the indicators used for this purpose, we can refer to the Standard Deviation Index to show the scatter of continuous distributions in terms of unit of measurement, variance, which is the deviation between one of the data values and its average, amplitude of change means the distance between the smallest and largest values in the total available data and Quartile Deviation.
Since the dispersion criteria introduced, including standard deviation, depend on the unit of measurement of the data; you can use the coefficient of variation to compare the dispersion of two communities with different units and to express the dispersion rate as a percentage. Low dispersion indicates the homogeneity of the community and having a lower coefficient of variation due to the greater accuracy of the results obtained from the mean index, indicates a better community. The coefficient of variation is used only for relative scales and it is not possible to use it to measure values that can take a negative value.
In some studies, correlation methods should be used to determine the relationship between the two variables. The scale for measuring variables has a large effect on the calculated correlation coefficient.
In calculating the correlation coefficient, the type of scale for measuring variables has a great impact and depending on the type of variable, the correlation coefficient may have different values. These coefficients are usually obtained by software.
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Regression is a special method used to study the contribution of independent variables in predicting the dependent variables. This analysis is a method for modeling the relationship between variables as well as examining them. And it is interesting to know that the application of regression does not end with statistical analysis but also in other fields; because the science of predictingis considered by most sciences and professions in the world.
There are certain types of regression, including linear, curvature, logistic regression, and analysis of covariance, which can be used in both descriptive research and experimental variation.
As mentioned in the regression section, analysis of the covariance matrix or correlation matrix is one of the correlation analyses. Two of the most famous types of these analyses are:
1- Structural equation model to study the relationships between variables
2- Factor analysis model to understand the underlying variables of a phenomenon in two categories of exploratory and confirmatory.