Statistics all notes:

First vaneko moments ? Moment vaneko k ho ? Physics ma Force * Distance, like seesaw ma hunxa hai. Yesma chai k xa vanni center kata xa vanni kura hunxa ni.

Tesari nai moment le ni center bata kati tada vanni kura xa.

Moment ko kura yo video bata herni :

https://www.youtube.com/watch?v=v-PyQ1Nmcfs

Ani variance mean and standard deviation kura : https://www.youtube.com/watch?v=SzZ6GpcfoQY

Moment generating function :

Binomial distribution :

Non — Parametric Test

In statistics, a non-parametric test is a type of statistical test that makes fewer assumptions about the distribution of the underlying population from which the sample is drawn compared to parametric tests. Parametric tests, such as t-tests and analysis of variance (ANOVA), assume that the data follows a specific probability distribution (often normal distribution) and that certain parameters can be estimated from the data.

Non-parametric tests are used when the assumptions of parametric tests cannot be met or when the data is on an ordinal or nominal scale. These tests are sometimes referred to as distribution-free tests because they don’t rely on assumptions about the shape of the population distribution.

Here are some common non-parametric tests:

1. Mann-Whitney U Test (Wilcoxon Rank-Sum Test): Used to compare two independent groups when the dependent variable is ordinal or continuous, but not normally distributed. (Non—parameter alternatives of t-test ). Its purpose is to test the null hypothesis that the two samples have similar median or, conversely, whether observations in one sample are likely to have larger values than those in the other sample. The t-test of unrelated samples is a parametric equivalent to the Mann-Whitney U-test.
2. Kruskal-Wallis Test: An extension of the Mann-Whitney U Test, this non-parametric test is used to compare more than two independent groups.
3. Wilcoxon Signed-Rank Test: Used to compare two related groups, often in a repeated measures design.
4. Friedman Test: An extension of the Wilcoxon Signed-Rank Test for more than two related groups.
5. Chi-Square Test: Used for categorical data to assess the association between two categorical variables. It includes tests like Pearson’s chi-square test and Fisher’s exact test.

Non-parametric tests are especially useful in situations where the assumptions of parametric tests are violated or when dealing with data that does not meet the requirements for parametric analyses. However, they may have less statistical power than their parametric counterparts, particularly when the assumptions of parametric tests are reasonably satisfied. Choosing between parametric and non-parametric tests depends on the nature of the data and the specific requirements of the analysis.

Type of data :

1. Discrete Data: Discrete data encompasses values that are exact and countable. Examples include:

• The number of flights in an hour.
• The count of roses on each plant in a garden.
• The bag sizes of employees in a company.

2. Continuous Data: Contrary to discrete data, continuous data can assume any numerical value. Illustrations include:

• The length of a pencil, ranging from 7cm to 9.56cm.
• The mass of a chocolate cake.
• The time is taken by a person to finish homework.

3. Nominal Data: Nominal data is organized categorically and lacks a numerical hierarchy. It includes:

• Characteristics like fat or thin in individuals.
• Hair color.
• Gender.
• Religion.

4. Ordinal Data: Ordinal data involves ranking items in order, comparing their positions. Examples comprise:

• Expressions of happiness: very happy, happy, unhappy, very unhappy.
• Degrees of liking: strongly like, like, neutral, dislike, strongly dislike.

5. Interval Data: Interval data allows for calculations and comparisons of size differences. Instances include Dates, temperature in Fahrenheit, and Years.

6. Ratio Data: Similar to interval data, ratio data provides information concerning an absolute zero and allows multiplication and division. Examples are Mass. , Length, Distance, Speed.

Bayes Theorem : Revised form of conditional probability.