Introduction
Statistics is a branch of mathematics, aimed at collecting and analyzing data via different methods such as analysis of variance, kurtosis, skewness or regression analysis. Nowadays, statistics helps processing data with a help of creating various charts that in turn help visualizing complex data sets. There are two major types of statistics, descriptive statistics and inferential statistics. Descriptive and inferential statistics require proper hypothesis formation and thus proper selection of the statistical tests that in turn have to be analyzed and interpreted successfully.
Descriptive Statistics
Descriptive statistics implies application of various coefficients that simplify process of data processing and aggregation (Trochim, 2006a). With a help of coefficients, one can analyze either entire data set or its fraction. Descriptive statistics help analyzing various trends in data, that is to say indirect dependencies. It is possible to calculate mean indicator of some complex process, while analyzing all maximal and minimal deviations of the data set.
Inferential Statistics
Inferential statistics helps making conclusions within the framework of uncertainty, caused by lack of data. With a help of inferential statistics, one can make conclusion while having only sample of some fraction of population surveyed. Inferential statistics is good at comparing two sets of data. Types of inferential statistical methods are discriminant function analysis, cluster analysis, multidimensional scaling, regression analysis, Analysis of Covariance (ANCOVA), Analysis of Variance (ANOVA), t-test within the framework of the General Linear Model (Trochim, 2006b).
Hypothesis Development & Testing
The aim of every statistical research is to prove or debunk a research hypothesis, based on subjective assumptions of the researchers. Since hypotheses are mostly subjective, they require further testing to make sure they are credible. While one group of students could be a sample for the statistical research, all students of a country could be population for extrapolating data received after testing hypothesis in case of a sample (“Hypothesis Testing,” 2013).
Selection of Appropriate Statistical Tests
Should data be interpreted while grouping samples in pairs?
What if grouping samples in pairs will distort final conclusion?
Is there obvious correlation between variables?
Do data sets correspond to each other?
Do survival plots or time-to-event tendencies vary a lot?
After answering aforementioned five questions, one can choose the right statistical method for his/her research.
Evaluation of statistical results
Evaluation of statistical results consists of four steps such as identification of goals and formulation of expectations, determination of analytical techniques for performing data analysis, assessment of the results against both goals and expectations, review of the goals and start of another statistical test if needed, according to Australian Bureau of Statistics (2010).
The results of the statistical test depend on the trustworthiness of the hypothesis that in turn depends on numerous factors, and all of them have to be taken into account in order to achieve the most accurate result of the statistical test. For example, if analyzing performance of various groups of students, not only curriculum has to be taken into account, but also socioeconomic environment of the neighborhood or even environment of separate families (“A Guide for Using Statistics for Evidence Based Policy,” 2010). Without taking into account external factors such as socioeconomic factors, any statistical research of the impact of the curriculum on the performance of the students may be inaccurate and thus misleading.
Various analytical techniques may be applied for researching the same issue. Graphical analysis is one of the most popular analytical techniques since it implies both processing of data and its further visualization, that is to say presentation of numerous figures into a chart, easy for understanding even by non-proficient reader. Graphical analysis helps understanding all ups and downs of some process, as well as mean indicators to help predict future trends.
While mean indicator should be detected and processed, mean indicators provides approximate understanding of the situation. As for estimating standard deviation of a data set, it can be sometimes hard to present it as a single number (Rumsey, 2010). The smaller standard deviation, the closer all data parameters to mean indicator. Small standard deviation itself can be an objective that should be reached in the course of the statistical research (Rumsey, 2010). For example, quality control test would imply an objective of achieving small standard deviation. In this case, all samples are of the same quality. On the contrary, significant standard deviation would mean many parts are simply defective and thus cannot be supplied.
Conclusion
Every statistical test requires hypothesis, which in turn has to be either confirmed or debunked in the course of the statistical test. While some tests can require minimal standard deviation as a final goal, others may imply different goals. Graphical analysis technique offers more comfortable process of interpreting results of the statistical tests, but various types of charts may emphasize different aspects of the data sets. For example, data spread can be graphically depicted as an array of dots, while mean indicator would be a line across an array of dots to show some median trend all over the data set.
References
Nayak, B., & Hazra, A. (2011). How to choose the right statistical test? Indian Journal of Ophthalmology, 59(2), 85.
Rumsey, D. (2010). How to Interpret Standard Deviation in a Statistical Data Set. Retrieved January 07, 2017, from http://www.dummies.com/education/math/statistics/how-to-interpret-standard-deviation-in-a-statistical-data-set/
Trochim, W. (2006a). Descriptive Statistics. Retrieved January 06, 2017, from http://www.socialresearchmethods.net/kb/statdesc.php
Trochim, W. (2006b). Inferential Statistics. Retrieved January 06, 2017, from http://www.socialresearchmethods.net/kb/statinf.php
Australian Bureau of Statistics (2010). A Guide for Using Statistics for Evidence Based Policy. Retrieved January 06, 2017, from http://www.abs.gov.au/ausstats/abs@.nsf/lookup/1500.0chapter82010
Lund Research Ltd (2013). Hypothesis Testing. Retrieved 06, 2017, from https://statistics.laerd.com/statistical-guides/hypothesis-testing.php
