Hypothesis Testing, Confidence Interval, Significance Level and P Value IN SHORT
Hypothesis Test
Hypothesis means assumptions. So in the hypothesis test, we assume two or more exclusive statements on population using sample data points.
Exclusive statements mean one part cannot be part of another one. For example, let’s consider in population we have two genders (male/female) so males cannot be part of females and vice versa.
So there are 2 kinds of hypothesis: Null hypothesis and Alternate hypothesis
The null hypothesis suggests there is no statistically significant relationship between the two variables. The alternate hypothesis suggests there is some statistically significant relationship between the two variables
For example, senior citizens will invest in fixed deposits (Yes/No)?
Null hypothesis: There is no relationship between the age of the customer and fixed deposit investment.
Alternate hypothesis: There is some kind of relationship between the age of customers and fixed deposit investment.
On what basis do we accept or reject the null hypothesis ?
Based on the level of significance and confidence interval.
The level of significance or significance level is the probability with which we will reject the null hypothesis when it is true. The confidence interval is the probability with which we will accept the null hypothesis when it is true.
So in short, a 95% confidence interval will have a 5% level of significance.
Confidence Interval (1 — Alpha or 1 — Significance Level)
The confidence interval tells us how much we are confident about the result
The confidence interval is denoted by one minus alpha (CI = 1 — alpha)
For instance, a 95% confidence interval means if we repeat the same experiment or the survey over and over again 95% of the time it will match the result
For example, suppose we say in the country approximately 30 to 35 lakhs senior citizens reinvest their Fixed Deposits with a 95% confidence interval. It means if we repeat the survey with the same technique there will be 95% of the time result will fall between 30 to 35 lakhs for senior citizens reinvesting their fixed deposits.
Level of Significance or Significance Level (Alpha)
The significance level shows how likely a pattern in the details is due to chance.
The level of significance or significance level is denoted by alpha (SL = alpha), most statistical packages show the P value of significance level.
Suppose in a dataset, the P value of the variable is 0.09 then 91% chance there is some kind of relationship between the independent variable and dependent variable.
Factors affecting Confidence Interval
- Variation: If variation within samples is almost similar, then data will have low variations which will lead to a narrow confidence interval. If samples have a lot of variation will lead to a wider confidence interval.
- Sample Size: Small sample size will lead to high variation between different sample sets which will lead to a larger confidence interval but a large sample size will have more similarities between the different sample sets which will lead to a smaller confidence interval.
P Value
P value is a probability value
For example, consider laptop touchpads we say exactly in the middle of the touchpad click P value is 0.8 meaning out of 100 times 80 times we will touch in the middle of the touchpad. Suppose for the top left corner touchpad click we have a P value of 0.1 means out of 100 times 10 times will touch the top left corner of the touchpad.
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