P Values Z Values and T Values

P-Values

Lets us start by Understanding what is P-values.

p-value to weigh the strength of the evidence to see if it’s statistically significant. If the evidence supports the alternative hypothesis, then we’ll reject the null hypothesis and accept the alternative hypothesis.

Before going more further let me explain few terms required to understand P-Values.

Hypothesis testing — Hypothesis testing is used to test the validity of a claim (null hypothesis) that is made about a population using sample data. The alternative hypothesis is the one you would believe if the null hypothesis is concluded to be untrue.

Lets us take an example to understand it more properly

Suppose I have two medicine for covid 19 Treatment and I want to know if they are different or not

Suppose we did a test on around 1000 people to test whether both drugs are the same or not and we get the result as –

In this condition, it is obvious that drug A is different than Drug B.

But now let us take a scenario where –

Here we cannot be sure whether drugs A and B are different. So, in this case, we can use P-value in knowing how different is Drug A from B.

P-value will vary between 0 to 1 closer the value of p to 0 the more confident we have that Drug A and B are different.

In practice a commonly use threshold for P-value is 0.05 it means that if there is no difference between A and N and if we did this exact same experiment a bunch of times, then only 5% of those experiments would result in the wrong decision.

Like in the above example if we get P = 0.9 then is sure that Drugs A and B are the same. But if we get p = 0.04 then we can say that they both are different.

Z- Score

Z-score is a statistical measure that tells you how far is a data point from the rest of the dataset. In a more technical term, I can say that Z-score tells how many standard deviations away a given observation is from the mean.

Example — For example, a Z score of 2.5 means that the data point is 2.5 standard deviation far from the mean.

It is calculated as Z score = x-mean / Standard deviation

T — values

Basically, it compares the difference between the groups with the difference within the groups.

Now the question arises how do we know if the T-value is big enough to show a difference.

Each t-value has an R-value which we have discussed above, The P-value tells us the likelihood that there is a real difference.

The question which I will ask being an Interviewer -

1) How we can calculate P-value?

Ans — The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis.

2) Is a P-value of 0.001 can be considered good for comparing and what is the standard P-value that can be said correct?

Ans — Yes P-value of 0.001 can be considered Good. A P-value of 0.05 is considered standard although it can vary according to different conditions.

3) What does the Z-Score of -2 tell us?

Ans — Z-score of -2 tells us that we are 2 standard deviations to the left of the Mean.

4) What is the use of STANDARD NORMAL TABLE in the Z-score?

Ans — This Table tells us the total amount of are contained to the left side of any value of Z fo this table the top row and the 1st column to Z values and all number in the middle correspond to areas.

5) How we can know T-value is Big-enough?

Ans Each T value has a corresponding P-value and the P-value is the probability that the pattern of data is the sample could be produced by random data.