Table of Contents

# 2 Main branches of statistics

Statistics is the study tasked with developing and studying the ways of data collection, data analysis, data interpretation, and data presentation for empirical data. In addition, statistics is a way of getting conclusions from data.

There are two main branches of statistics which include: **Descriptive statistics** and **inferential statistics**. They are further subdivided into groups for better data collection, analysis, interpretation, and presentation.

**Descriptive statistics.**

It is brief descriptive coefficients that provide a summary of the sample given. Descriptive statistics allow you to describe your data based on its properties. It is grouped into four major types, measures of frequency, measures of central tendency, measures of dispersion and variation, and measures of position. Descriptive statistics are essential since if data were presented raw, it would be hard to visualize what the data was showing.

**Measures of frequency.**

These are used to show how often something often occurs. They are represented in count, percent, and frequency. They are used when one wants to show how often a response is given.

**The measure of central tendency.**

These are ways of summarizing a group of data by describing how the scores are spread. Mean, mode, and median are the most common ways of measuring central tendency. They locate the distribution at various points. They are used when you want to show how an average or most common response is given.

**Measures of dispersion and variation.**

They are represented in range variance and standard deviation. They identify the distribution of scores by the starting intervals.

Range=High/low points

Variance or standard deviation =difference between the observed score and mean

These are used to show how spread the data is and how they spread to affect the mean.

**Measures of position**

These are the percentile and quartile ranks that describe how the data fall in relation to one another. They are represented using standardized scores. They are used when there is a need to compare a score to a normalized score.

**Inferential statistics.**

Inferential statistics allows one to make predictions or inferences from data. Through inferential statistics, one may draw predictions on what a population may think or how it has been affected by taking a sample. Inferential statistics uses sample data because it’s cheap and less tedious. Sapling should be done in unbiased methods and at random so that the conclusions and inferences can be considered valid. Several kinds of inferential statistics can be calculated. The common types are as follows.

**t-tests**

This is a test used to compare means. There are three basic types of t-test one-sample t-test, independent sample t-test, and dependent sample t-test.

**One sample t-test**

**One sample t-test**

One sample t-test compares data to the mean of some known populations.

**Independent sample t-test**

**Independent sample t-test**

An independent sample t-test is used to compare two separate non-related samples.

**Dependent sample t-test**

A dependent sample t-test can be used to compare data from related groups or the same population over time. They are used mainly in the case of a pre-test and post-test setup.

**ANOVA (Analysis of variance)**

ANOVA is a statistical analysis used to compare means. Compared to a t-test in which you can compare two means in ANOVA, we can compare multiple means at the same time. Two types of ANOVA are one-way ANOVA and factorial ANOVA.ANOVA compares numerous groups on the same variable.

**One-way ANOVA.**

One-way ANOVA is used to compare three or more groups in the same dimension .this is the same as the independent sample t-test.

**Within groups ANOVA**

It compares data from related groups or the same population over time. It is almost similar to the dependent sample t-test with more data sets.

**Factorial ANOVA**

Factorial ANOVA is used when there are two or more variables and you are studying the interactions between these factors. Essentially you are comparing the means of the various combination of aspects.

**Regression**

Regression analysis involves making predictions on an outcome variable based on knowledge of some predictor variable. It is used to find trends in data. It is a way that uses mathematics to sort out the variables which have an impact. There are two types of regression analysis linear regression analysis and logistic regression analysis.

**Linear regression analysis**

Linear regression shows the relationship between two variables in a linear algorithm. There are two main types of linear regression: simple linear regression, where only one independent variable changes and leads to different values of the other variable, and multiple linear regression, which is used to show the relationship between one dependent variable and two or more independent variables. Linear regression representations are usually done graphically using scatter plots but can also be demonstrated by other linear types of graphs.

**Logistic regression analysis**

Logistic regression analysis is where the dependent variable is categorical. Logistic regression is conducted when the dependent variable has only two possible values.

**Analysis of covariance (ANCOVA)**

This is an ANOVA where we have a continuous covariate. A covariate is a constant independent variable. ANCOVA is a blend of ANOVA and regression. ANCOVA is an inferential statistics model useful when studying the differences in mean values of the dependent variables.

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