LESSON 5 : STATISTICAL HYPOTHESIS TESTS

INTRODUCTION
Statistical hypothesis testing is an intrinsic tool for making inference about a defined population in Statistics. It entails drawing conclusion from sample data based on statistical statements made about the sample data. This statement or claim is called Statistical hypothesis.

Listed as lesson 5 of the 7days of Statistics challenge from the desk of DSN AIPlus UI below are the objectives of the lesson

OBJECTIVES

• Understand the basic concepts of statistical hypothesis testing.
• Understand how to set up an hypothesis from a problem statement.
• Understand the concept of p-value in hypothesis testing.
• Understand the concept of Type 1 and Type 2 error.

TYPES OF HYPOTHESIS

• Null hypothesis – as the name implies ‘NULL’, this is the statement of no difference between the hypothesised value and the observed value. It renders a statistical hypothesis insignificant and it is symbolically denoted as Ho.
• Alternative hypothesis – this is the hypothesis contrary to the null hypothesis. The alternative hypothesis renders a statistical hypothesis significant, which means, it assumes that the hypothesised value significantly deviates from the observed value. It is symbolically denoted as H1.

TYPES OF ERROR

Errors are likely made when drawing conclusions from statistical hypothesis testing, the errors are of two types namely;

• Type 1 error - this type of error is committed when when a true null hypothesis is rejected in favour of the false alternative hypothesis, meaning accepting H1 is true when actually Ho is true.
• Type 2 error – this type of error is committed when a false null hypothesis is accept in denial of a true alternative hypothesis, meaning accepting Ho is true when actually H1 is true.

P-VALUE
p-value is the probability of getting the sample value while Ho is true, it a probability value ranging from 0 to 1 which measures how strong or how weak the observed value will be gotten assuming that Ho is true. This implies that the higher the p-value, the stronger the chances of getting observed value and vice versa. P-value is compared directly with the stated level of significance which is mosly taken as 5%(0.05).

Below is a real life example to determine if the mean year a university student admitted in year 2016 will graduate is the same irrespective of year of study and extra year(ranging from 1 to 3) at 5percent level of significance

From above, comparing the p-value directly with the level of significance (0.05). p-value > 0.05. It is safe to accept the null hypothesis and conclude that the statistical hypothesis is insignificant.

TASK

• Think of a real life problem statement,simulate random numbers with respect to the problem statement, run statistical hypothesis test and explain your conclusion.
• Read more about sided tests.
• Read further about statistical hypothesis testing.