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Statistics is a branch of mathematics, which helps us to derive sense from a bunch of data. It is concerned with the collection, analysis and interpretation of data using theories of mathematics and computational tools.The inferences from this analysis helps us to arrive at a pertinent conclusion. The word ‘Statistics’ is believed to have been derived from a number of sources, such as the Latin word statisticum collegiumwhich translates to mean a council of state, the Italian word statista meaning a politician and the German Book Statistik. In terms of origin, this discipline is not a modern branch of study but has been there for centuries. The use of statistical concepts has been in use as far as the 5th Century BC. Ancient rulers used the concepts of statistics to gather data about population and statecraft to make better decisions.
The definition of Statistics has undergone many changes with time. The earliest definition restricted its field to only counting and averages. However, as understanding about the dynamic nature of this field grew, the definitions also changed and now it is defined as a versatile branch of scientific study with theories, principles, methods and tools to analyse and interpret a complex set of data. The first mention of statistical analysis and inference, has been held to be in the work of John Graunt, “Natural and Political Observations” in 1662. Though there have been many scientists who have contributed to making this subject, as it is known today, the British scientist Sir Ronald Fisher isconsidered to be the Father of Modern Statistics. The important underlying ideas in Statistics are probability and variance. Probability is the uncertainty of an event or data and variation refers to the scope of dispersion in a given set of data.
Methods of Statistical analysis refer to the various ways in which statistical measurement is achieved. The following are the main methods used:
Statistics have emerged to be an important field of study and discipline in recent years. The use of statistics in almost all areas of life has increased its importance. Statistics is not only used in areas of research and science but also finds application in practical life as well. Statistics is used in the areas of administration, management and decision taking. Statistical analysis are used by governments to make informed decisions and affect their policy making. The policies affect us all and therefore it is necessary that statistical analysis is done correctly. The scope of statistics is ever increasing and is not only restricted to the following fields:
A one sample t-test in statistics is used to verify whether there is any significant statistical difference between the actual mean value of a sample and the generally accepted or hypothesized mean value. T-tests can be performed with small samples only, where n should be lesser than 30. An instance of one sample t-test can be a case where it is known that average weight of white new born babies in the US is 3410 gm, and a sample of the weight of black new born babies is used to find the mean so as to see if they differ significantly from the average weight of white babies.
A binomial test in statistics is used when a test has two possible results, such as either success or failure, and there is a generally accepted idea (or hypothesis) about which outcome has a greater probability of occurring. A binomial test helps to find out if the outcome is different from what was expected. The key purpose is to figure out if the difference between the actual and expected results are statistically significant or not. For instance, it can be hypothesized that 70% of Physics students are male, and on conducting a survey on 12 students, it can be found that 7 students are male. Now the difference in expected an actual result is evident from this given data but the binomial test would help to establish whether this difference is statistically significant enough or not.
A one sample median test is aimed to find whether there is statistically relevant difference between the actual median of a sample and the expected or hypothesized median. To conduct the median test, it is crucial to first find the median of a given sample, which can be done by organizing the data in descending order, that is from the highest numerical value to the lowest, and the value which stands right in the middle of this ranked data is to be considered the median.
This test is applicable when there is a one categorical variable available from a single population. This test helps to establish whether the concerned set of data is in harmony with the hypothesized distribution of data. This test is ideal when 3 specific conditions are met. Firstly, the sample should be collected following simple random sampling method. Secondly, the variable which is being studied must be categorical. Thirdly, number of sample observations at every level of the variable must be a minimum of 5. The test is conducted in four parts where the hypothesis is stated, an analysis plan is formulated, sample data is analysed accordingly, and results are interpreted. For example, a pack of M&M can be assumed to contained 600 pieces, and since a standard package contains 6 colours of candies, it can be hypothesized that there are 100 candies of each colour. However, on analysing it can be discovered that the six different colours of candies are not equally distributed as assumed, and significance of this difference is distribution can be found through chi square goodness of fit test.
This test is the non-parametric alternative for independent samples t-tests; they can be performed when the dependant variable is not assumed to be a normally distributed interval variable. Parametric tests set down certain parameters like ones about normal distribution, as a consequence of which certain samples become unsuitable for parametric tests. Most parametric statistical tests have an alternative non-parametric test ideal for deviant samples and Mann-Whitney-Wilcoxon test is one such test. It is also known as the Mann-Whitney U Test or Wilcoxon Rank-Sum Test. It is a test of the null hypothesis that states there is equal probability that a randomly selected value from one sample will be greater or less than a randomly selected value from another sample.
One-way ANOVA or Analysis of Variance is used to compare the mean of three or more samples by using F distribution. One-way ANOVA works only for numerical response data which is commonly a single variable, and categorical or numerical input data, which is compulsorily one variable, thereby giving the name ‘one-way’ to the technique. It can reveal if there are significant differences between three or more independent groups. For instance, one-way ANOVA can be used to find if performance of students in an exam varied based on the test anxiety levels of students by categorising students into low, medium, and high stress groups.
Fisher’s Exact Test is effective in finding whether there are non-random associations between two categorical variables. It is used in the analysis of contingency tables and is more effective than chi-square test and G-test when the sample size is a small one. The test is named after its inventor Ronald Fisher. It is called an exact test because deviation from a null hypothesis can be calculated in exact terms without having to depend upon approximations. For instance, let’s assume that a study is conducted among 50 patients and it is found that percentage of patients who took drug A and got cured was higher than percentage of patients who took drug B. In such a situation, Fisher’s Exact Test would reveal whether the observation made is statistically significant or not.
Kruskal Wallis H test is a non-parametric test based on rank and it can be implemented to determine whether there exist statistically relevant differences between two or more than two groups of independent variables on an ordinal or continuous dependent variable. It compares two or more independent samples of different or equal sample size, and it is used to evaluate if the samples originate from same distribution.
Friedman test is the nonparametric alternative for one-way ANOVA and is used for detecting the difference in treatments across multiple attempted tests. It is employed for finding differences between groups when the dependent variable being used is ordinal. In the process, each row is ranked together, and then values of each row are considered in a column-wise manner.
Regression analysis in statistical modelling comprises of a number of statistical processes to determine the relationship (if any) between a dependent variable and an independent variable. Linear Regression is typically a linear approach that attempts to frame the extent of relationship between a dependent variable or scalar response, and one or more independent or exploratory variables. For instance, linear regression would be useful is estimating the relationship between variables like gender, diet, and age on a variable like height.
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