Models of Statistics

Various models of Statistics are used to measure different forms of data. Some of the models of the statistics are added below:

• Skewness in Statistics
• ANOVA Statistics
• Degree of Freedom
• Regression Analysis
• Mean Deviation for Ungrouped Data
• Mean Deviation for Discrete Grouped data
• Exploratory Data Analysis
• Causal Analysis
• Standard Deviation
• Associational Statistical Analysis

Let’s learn about them in detail.

Skewness in Statistics

Skewness in statistics is defined as the measure of the asymmetry in a probability distribution that is used to measure the normal probability distribution of data.

Skewed data can be either positive or negative. If a data curve shifts from left to right is called positive skewed. If the curve moves towards the right to left it is called left skewed.

ANOVA Statistics

ANOVA statistics is another name for the Analysis of Variance in statistics. In the ANOVA model, we use the difference of the mean of the data set from the individual data set to measure the dispersion of the data set.

Analysis of Variance (ANOVA) is a set of statistical tools created by Ronald Fisher to compare means. It helps analyze differences among group averages. ANOVA looks at two kinds of variation: the differences between group averages and the differences within each group. The test tells us if there are disparities among the levels of the independent variable, though it doesn’t pinpoint which differences matter the most.

ANOVA relies on four key assumptions:

1. Interval Scale: The dependent data should be measured at an interval scale, meaning the intervals between values are consistent.
2. Normal Distribution: The population distribution should ideally be normal, resembling a bell curve.
3. Homoscedasticity: This assumption states that the variances of the errors should be consistent across all levels of the independent variable.
4. Multicollinearity: There shouldn’t be significant correlation among the independent variables, as this can skew results.

Additionally, ANOVA assumes homogeneity of variance, meaning all groups being compared have similar variance.

ANOVA calculates mean squares to determine the significance of factors (treatments). The treatment mean square is found by dividing the treatment sum of squares by the degrees of freedom.

It operates with a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis generally posits that there’s no difference among the means of the samples, while the alternative hypothesis suggests at least one difference exists among the means of the samples.

Degree of Freedom

Degree of Freedom model in statistics measures the changes in the data set if there is a change in the value of the data set. We can move data in this model if we want to estimate any parameter of the data set.

Regression Analysis

Regression Analysis model of the statistics is used to determine the relation between the variables. It gives the relation between the dependent variable and the independent variable.

There are various types of regression analysis techniques:

1. Linear regression: This method is used when the relationship between the variables is linear, meaning the change in the dependent variable is proportional to the change in the independent variable.
2. Logistic regression: Used to predict categorical dependent variables, such as yes or no, true or false, or 0 or 1. It’s used in classification tasks, such as determining if a transaction is fraudulent or if an email is spam.
3. Ridge regression: Ridge regression is a technique used to combat multicollinearity in linear regression models. It adds a penalty term to the regression equation to prevent overfitting. It’s most suitable when a data set contains more predictor variables than observations.
4. Lasso regression: Similar to ridge regression, lasso regression also adds a penalty term to the regression equation. However, lasso regression tends to shrink some coefficients to zero, effectively performing variable selection.
5. Polynomial regression: Uses polynomial functions to find the relationship between the dependent and independent variables. It can capture nonlinear relationships between variables, which may not be possible with simple linear regression.
6. Bayesian linear regression: Bayesian linear regression incorporates Bayesian statistics into the linear regression framework. It allows for the estimation of parameters with uncertainty and the incorporation of prior knowledge into the regression model.

How to create chart and table

Choose the right chart type: Different chart types are better suited for different kinds of data. For example, bar charts are good for comparing categories, while line charts are good for showing trends over time.

Keep it simple: Don’t overload your chart with too much information. Make sure the labels are clear and easy to read.

Use clear and concise titles: Your chart title should accurately reflect the information being presented.

Use color effectively: Color can be a great way to highlight important data points, but avoid using too many colors or colors that clash.

Mean Deviation for Ungrouped Data

Suppose we are given ‘n’ terms in a data set x₁, x₂, x₃, …, x_n then the mean deviation about means and median is calculated using the formula,

Mean Deviation for Ungrouped Data = Sum of Deviation/Number of Observation

• Mean of Ungrouped Data = ∑_iⁿ (x – μ)/n

Mean Deviation for Discrete Grouped data

Let there are x₁, x₂, x₃, …, x_n term and their respective frequency are, f₁, f₂, f₃, …, f_n then the mean is calculated using the formula,

a) Mean Deviation About Mean

Mean deviation about the mean of the data set is calculated using the formula,

• Mean Deviation (μ) = ∑_{i = 1}ⁿ f_i (x_i – μ)/N

b) Mean Deviation About Median

Mean deviation about the median of the data set is calculated using the formula,

• Mean Deviation (μ) = ∑_{i = 1}ⁿ fi (x_i – M)/N

Exploratory Data Analysis

Exploratory data analysis (EDA) is a statistical approach for summarizing the main characteristics of data sets. It’s an important first step in any data analysis.

Here are some steps involved in EDA:

• Collect data
• Find and understand all variables
• Clean the dataset
• Identify correlated variables
• Choose the right statistical methods
• Visualize and analyze results

Exploratory Data Analysis (EDA) uses graphs and visual tools to spot overall trends and peculiarities in data. These can be anything from outliers, which are data points that stand out, to unexpected characteristics of the data set.

Following are the four types of EDA:

1. Univariate non-graphical
2. Multivariate non-graphical
3. Univariate graphical
4. Multivariate graphical

Causal Analysis

Causal analysis is a process that aims to identify and understand the causes and effects of a problem. It involves:

1. Identifying the relevant variables and collecting data.
2. Analyzing the data using statistical techniques to determine whether there is a significant relationship between the variables.
3. Drawing conclusions about the causal relationship between the variables.

Causal analysis differs from simple correlation in that it investigates the underlying mechanisms and factors that drive changes in variable values, rather than simply finding statistical links. It provides evidence of the causal relationships between variables.

Let’s look at some examples where we might use causal analysis:

• We want to know if adding more fertilizer makes plants grow better.
• Can taking a specific medicine prevent someone from getting sick?

To figure out cause and effect, we often use experiments like giving different groups different treatments and comparing results. These types of studies, called “randomized controlled trials,” are usually the best way to show that something caused a change.

Sometimes, other things can interfere with our understanding of cause and effect. For example, two things might appear connected because they both come from a third factor. This confusion is known as “confounding.” When confounding happens, it can lead us to wrongly think that one thing caused another when it really didn’t.

Standard Deviation

Standard Deviation is a measure of how widely distributed a set of values are from the mean. It compares every data point to the average of all the data points.

A low standard deviation means values are close to the average, while a high standard deviation means values spread out over a wider range. Standard deviation is like the distance between points but applied differently. Using algebra on squares and square roots, rather than absolute values, makes standard deviation convenient in various mathematical applications.

Associational Statistical Analysis

Associational statistical analysis is a method that researchers use to identify correlations between many variables. It can also be used to examine whether researchers can draw conclusions and make predictions about one data set based on the features of another.

Associational analysis examines how two or more features are related while considering other possibly influencing factors.

Some measures of association are:

Chi-square Test for Association

Chi-square test of independence, also called the chi-square test of association, is a statistical method for determining the relationship between two variables that are categorical. It assesses if the variables are unrelated or related. Chi-square test determines the statistical significance of the relationship between variables rather than the intensity of the association. It determines if there is a substantial difference between the observed and expected data. By comparing the two datasets, we can determine whether the variables have a logical association.

For example, a chi-square test can be done to see if there is a statistically significant relationship between gender and the type of product bought. A p-value larger than 0.02 indicates that there is no statistically significant correlation.

Correlation Coefficient

A correlation coefficient is a numerical estimate of the statistical connection that exists between two variables. The variables could be two columns from a data set or two elements of a multivariate random variable.

The Pearson correlation coefficient (r) measures linear correlation, ranging from -1 to 1. It shows the strength and direction of the relationship between two variables. A coefficient of 0 means no linear relationship, while -1 or +1 indicates a perfect linear relationship.

Here are some examples of correlations:

1. Positive linear correlation: When the variable on the x-axis rises as the variable on the y-axis increases.
2. Negative linear correlation: When the values of the two variables move in opposite directions.
3. Nonlinear correlation: Also called curvilinear correlation.
4. No correlation: When the two variables are entirely independent.

Statistics and its Types: Statistics is a branch of math focused on collecting, organizing, and understanding numerical data. It involves analyzing and interpreting data to solve real-life problems, using various quantitative models. Some view statistics as a separate scientific discipline rather than just a branch of math. It simplifies complex tasks and offers clear insights into regular activities. Statistics finds applications in diverse fields like weather forecasting, stock market analysis, insurance, betting, and data science.

In this article, we will learn about, What is Statistics, Types of Statistics, Models of Statistics, Statistics Examples, and others in detail.