Hypothesis Testing

 

What is hypothesis testing ?

It’s a statistical method that is used in making statistical decisions using experimental data. Hypothesis Testing is basically an assumption that we make about the population parameter

Ex : you say avg student in class is 40 or a boy is taller than girls.

all those example we assume need some statistic way to prove those. we need some mathematical conclusion what ever we are assuming is true.

1.         Why do we use it ?

A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. When we say that a finding is statistically significant, it’s thanks to a hypothesis test.

    What are Basics of hypothesis?

The basic of hypothesis is normalisation and standard normalisation. all our hypothesis is revolve around basic of these 2 terms.

concept of z-score comes in picture when we use standardised normal data.

Normal Distribution-

          A variable is said to be normally distributed or have a normal distribution if its distribution has the shape of a normal curve — a special bell-shaped curve

1.      The mean, median, and mode are equal.

Standardised Normal Distribution —

A standard normal distribution is a normal distribution with mean 0 and standard deviation 1

                    

Which are important parameter of hypothesis testing ?

Null hypothesis :- In inferential statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups

In other words it is a basic assumption or made based on domain or problem knowledge.

 

Example : a company production is = 50 unit/per day etc.

Alternative hypothesis :-The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. It is usually taken to be that the observations are the result of a real effect (with some amount of chance variation superposed)

Example : a company production is !=50 unit/per day etc.

 

Level of significance: Refers to the degree of significance in which we accept or reject the null-hypothesis. 100% accuracy is not possible for accepting or rejecting a hypothesis, so we therefore select a level of significance that is usually 5%.

This is normally denoted with alpha(maths symbol ) and generally it is 0.05 or 5% , which means your output should be 95% confident to give similar kind of result in each sample.

 

Type I error: When we reject the null hypothesis, although that hypothesis was true. Type I error is denoted by alpha. In hypothesis testing, the normal curve that shows the critical region is called the alpha region

Type II errors: When we accept the null hypothesis but it is false. Type II errors are denoted by beta. In Hypothesis testing, the normal curve that shows the acceptance region is called the beta region.

 

One tailed test :- A test of a statistical hypothesis , where the region of rejection is on only one side of the sampling distribution , is called a one-tailed test.

Example :- a college has ≥ 4000 student or data science ≤ 80% org adopted.

Two-tailed test :- A two-tailed test is a statistical test in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.

Example : a college != 4000 student or data science != 80% org adopted

 

P-value :- The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H 0) of a study question is true — the definition of ‘extreme’ depends on how the hypothesis is being tested.

If your P value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample gives reasonable evidence to support the alternative hypothesis. It does NOT imply a “meaningful” or “important” difference; that is for you to decide when considering the real-world relevance of your result.

Example : you have a coin and you don’t know whether that is fair or tricky so let’s decide null and alternate hypothesis

H0 : a coin is a fair coin.

H1 : a coin is a tricky coin. and alpha = 5% or 0.05

Now let’s toss the coin and calculate p- value ( probability value).

Toss a coin 1st time and result is tail- P-value = 50% (as head and tail have equal probability)

Toss a coin 2nd time and result is tail, now p-value = 50/2 = 25%

and similarly we Toss 6 consecutive time and got result as P-value = 1.5% but we set our significance level as 95% means 5% error rate we allow and here we see we are beyond that level i.e. our null- hypothesis does not hold good so we need to reject and propose that this coin is a tricky coin which is actually.

Degree of freedom :- Now imagine you’re not into hats. You’re into data analysis.You have a data set with 10 values. If you’re not estimating anything, each value can take on any number, right? Each value is completely free to vary.But suppose you want to test the population mean with a sample of 10 values, using a 1-sample t test. You now have a constraint — the estimation of the mean. What is that constraint, exactly? By definition of the mean, the following relationship must hold: The sum of all values in the data must equal n x mean, where n is the number of values in the data set.

So if a data set has 10 values, the sum of the 10 values must equal the mean x 10. If the mean of the 10 values is 3.5 (you could pick any number), this constraint requires that the sum of the 10 values must equal 10 x 3.5 = 35.

With that constraint, the first value in the data set is free to vary. Whatever value it is, it’s still possible for the sum of all 10 numbers to have a value of 35. The second value is also free to vary, because whatever value you choose, it still allows for the possibility that the sum of all the values is 35.

Degree of freedom =( n-1)