What are the 5 methods of statistical analysis?

Statistics is a mathematical study that deals with collection and analysis. steps include data collection, analysis of data, perception, and organization or summarization of data. Statistics is a form of applied mathematics that produces a set of studies from the obtained data.

This mathematical analysis makes the dataset applicable for real life. Statistics has its dominance in the field of psychology, geology, weather forecast, etc. the data is collected either in quantitative or qualitative form.

What are the 5 basic methods of statistical analysis?

Various datasets are with excessive data are categorized into different types. These datasets of studies are prepared by different methods of statistical analysis.

• Mean

Mean or average is the most commonly used method to perform the statistical analysis. It is generally used in regard to research, academics, and sports. The calculation of mean involves adding up the given numbers and dividing them by the number of items.

The mathematical formula of mean is given by

X=∑x/n

where,

∑x = sum of numbers

n = number of items

• Standard Deviation

Standard deviation is a method for statistical analysis that uses the spread of information around the mean. As when you are trying to calculate a standard deviation the most information used is by the mean.

The mathematical formula of Standard deviation is given by

[Tex]σ = \sqrt{\frac{∑(x – μ)2}{n}}[/Tex]

where,

n = number of data points in the population

σ = variance

μ = mean of the data

x = value of a dataset

∑ = sum of data

σ = symbol of standard deviation

• Regression

In statistical analysis methods, regression is a connection between an independent variable and a dependent variable. The lines used in the graphs of the regression chart show the connections between factors and time.

The mathematical formula of regression is given by

Y=a + b(x) is the equation of the slope.

Y = independent variable

b = slope

x = dependent variable

a = y-intercept

The formula is, 

Y_i = f (X_i, β) + e_i

Y_i = dependent variable

X_i = Independent variable

e = error terms

β = unknown parameters

• Hypothesis testing

Hypothesis testing is also widely known as ‘T Testing’ is a statistical analysis method that works on contrasting the given information against different assumptions. It is an estimation that is made for business purposes.

The mathematical formula of hypothesis testing is given by,

[Tex]Z= \frac{X-U}{SD/\sqrt{n}}[/Tex]

• Sample Size Determination

Sample size determination is a method of examining information from an excessive dataset. The given is so enormous that it is hard to gather exact information for every dataset.

Key Aspects of Statistical Analysis

Aspect	Description
Data Collection	Gathering data through various methods such as surveys, experiments, observations, or measurements.
Data Organization	Organizing and structuring collected data systematically, often using tables, graphs, or databases.
Descriptive Statistics	Summarizing and describing main features of data, including measures of central tendency, dispersion, and distribution.
Inferential Statistics	Making inferences or generalizations about a population based on sample data, using hypothesis testing and estimation.
Statistical Techniques	Applying various statistical methods like regression analysis, ANOVA, correlation analysis, and chi-square tests.
Data Interpretation	Interpreting results of statistical analysis in the context of research questions, drawing conclusions, and making recommendations.
Statistical Software	Utilizing specialized software like SPSS, R, Python, SAS, or Excel for conducting analysis efficiently and accurately.

Types of statistic data 

There are majorly two types of statistics data. They are descriptive statistics and inferential statistics. Let’s learn about these two types in more detail,

Descriptive Statistics

This statistic provides a description of the population through numerical, graphs or tables by using the given data. It is further categorized as, 

• The measure of central tendency
• Measure of variability

Inferential Statistics

This type of statistics makes predictions about the population based on the given sample data. Inferential statistics uses the method of probabilities to prepare a datasheet.

Sample Questions

Question 1: What are the requirements to find a standard deviation?

Answer:

There are the following requirements to find a standard deviation

• Determine the mean of the numbers within the data set
• For each number within the data set, subtract the mean and square the result (formula (x − μ)2).
• Calculate the mean of those squared differences
• Take the square root of the final answer

Question 2: What is an inferential statistical analysis used for?

Answer:

Inferential statistical analysis is used to study the relationship between variables and data which are used for making predictions or assumptions about the population.

Question 3: Find the mean value of the given data 4, 12, 16, and 24.

Answer:

Sum of the number(x) = 4 + 12 + 16 + 24 = 56

Number of items(n) = 4

Now,

X = ∑x/n

X = 56/4

X = 14 

5 Methods of Statistical Analysis – FAQs

What is descriptive statistics?

Descriptive statistics involves summarizing and describing the main features of a dataset, such as measures of central tendency (mean, median, mode), dispersion (variance, standard deviation), and distribution (histograms, frequency tables).

When is descriptive statistics used?

Descriptive statistics is used to understand the basic characteristics of a dataset, providing insights into its structure, variability, and distribution.

How does descriptive statistics differ from inferential statistics?

Descriptive statistics summarizes the data within a sample, while inferential statistics makes inferences or predictions about a population based on sample data.

What is inferential statistics?

Inferential statistics involves making inferences or generalizations about a population based on sample data, using techniques such as hypothesis testing, estimation, and prediction.

When is inferential statistics used?

Inferential statistics is used to draw conclusions, make predictions, or test hypotheses about a population based on observed sample data.

What are some common inferential statistical techniques?

Common inferential statistical techniques include regression analysis, analysis of variance (ANOVA), correlation analysis, chi-square tests, and t-tests.

What is regression analysis?

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables.

When is regression analysis used?

Regression analysis is used to predict the value of the dependent variable based on the values of the independent variables and to understand the strength and direction of the relationships between variables.

What are the types of regression analysis?

Common types of regression analysis include linear regression, logistic regression, polynomial regression, and multiple regression.

What is analysis of variance (ANOVA)?

ANOVA is a statistical technique used to compare means across two or more groups to determine whether there are significant differences between them.

When is ANOVA used?

ANOVA is used when comparing means across multiple groups, such as in experimental or survey research designs with categorical independent variables.

What are the types of ANOVA?

Common types of ANOVA include one-way ANOVA (for one categorical independent variable), two-way ANOVA (for two categorical independent variables), and factorial ANOVA (for multiple independent variables).

What is the chi-square test?

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables.

When is the chi-square test used?

The chi-square test is used when analyzing categorical data to determine whether observed frequencies differ significantly from expected frequencies.

What are the types of chi-square tests?

Common types of chi-square tests include the chi-square test for independence (for testing association between two categorical variables) and the chi-square goodness-of-fit test (for comparing observed and expected frequencies).