Understanding Hypothesis Testing

Hypothesis are statement about the given problem. Hypothesis testing is a statistical method that is used in making a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
Example:
You say an average student in the class is 30 or a boy is taller than girls. All those are an example in which we assume or need some statistic way to prove those. We need some mathematical conclusion whatever we are assuming is true.

Need for Hypothesis Testing
Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, it is thanks to hypothesis testing.

Parameters of hypothesis testing

  • Null hypothesis(H0): In statistics, the null hypothesis is a general given statement or default position that there is no relationship between two measured cases or no relationship among groups.
    In other words, it is a basic assumption or made based on the problem knowledge.
    Example: A company production is = 50 unit/per day etc.
  • Alternative hypothesis(H1): The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis.
    Example : A company production is not equal to 50 unit/per day etc.
  • Level of significance
    It refers to the degree of significance in which we accept or reject the null-hypothesis. 100% accuracy is not possible for accepting a hypothesis, so we, therefore, select a level of significance that is usually 5%. This is normally denoted with \alpha 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.
  • P-value
    The P value, or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.

Example :
Given a coin and it is not known whether that is fair or tricky so let’s decide null and alternate hypothesis

  • Null Hypothesis(H0): a coin is a fair coin.
  • Alternative Hypothesis(H1) : a coin is a tricky coin.
  • \alpha = 5% or 0.05
  • Now let’s toss the coin and calculate p-value (probability value).

  • Toss a coin 1st time and assume that result is head- P-value = 50% (as head and tail have equal probability)
  • Toss a coin 2nd time and assume that result again is head, now p-value = 50/2 = 25%

and similarly, we Toss 6 consecutive time and got the result as all heads, now 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 because it gives us 6 consecutive heads.

Error in Hypothesis Testing

  • Type I error: When we reject the null hypothesis, although that hypothesis was true. Type I error is denoted by alpha.
  • Type II errors: When we accept the null hypothesis but it is false. Type II errors are denoted by beta.
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