Statistics 101 — P Value, Z Value

Saahil Sharma
Aug 24, 2017 · 3 min read

Lets figure out what the wonder is P Value. But before we do that, lets see what the Hypothesis Testing is?

A Hypothesis Testing is a procedure where you make an assumption about something, often called as Null Hypothesis and then perform various tests to check if the assumption is believed to be true or not?

Since, we are talking the statistics language, we will be using null hypothesis instead of assumption which is kind of a general term and may have different meaning in different context.

Now, you have a null hypothesis and you started performing various tests to make a base for it. But suppose, in your tests, you get to know that the observations recorded are creating a different story altogether. At first, you start to feel strongly about null hypothesis, but later after this incident, you are kind of ready to reject the null hypothesis. Hence, you start to make an Alternative Hypothesis and check if that hypothesis is correct or not.

This rejection of null hypothesis and accepting the alternate hypothesis is done using the P value which will discuss with an easy example.

P-Value or Probability Value is the calculation of probability of the observations to check if the observed values are same or extreme when the null hypothesis is true.

Now lets take an example of coin toss.

My null hypothesis is that the coin is not biased. So, now i take observations of tossing the coin and recording if the face value of the coin is heads or tails. Under normal circumstances, the probability is 1/2 for both the face values. but after taking 5 observations, i get to know that all the outcomes are Tails. at first outcome of tail, my p-value will be 0.5 or 1/2. but as i proceed, the value keeps on decreasing from 0.25, 0.12, and ultimately at 0.1. Hence, i confer that my null hypothesis is false and i reject it.

Z-Score or Z-Value or Standard Score is the value of the distance between the mean of the distribution and the raw score calculated in standard deviation.

Lets look at this with different perspective. lets generalize the whole term into layman terms for better understanding with an example because “To understand something, always understand it with an example”.

Let’s say, we have the score of IQ for the whole population and we need to find out how much percentage of the population has the IQ in the range of 70 and 130 (considering we have the mean of 100 and standard deviation of 15).

For Reference purpose only

Now to find out the Z Score, we us this mathematical formula —

Hence, by using this formula, our Z Score comes to (-2.00, 2.00) where x is the value of 70 and 130 respectively.

Now we know the Z Score, but our main problem is to find the percentage of people falls under the range of 70–130. There are two ways to calculate this-

  1. Use the Z table and find the value which will be 0.4772
  2. Standardize the whole distribution where your mean becomes 0 and standard deviation becomes 1 and then find the value of 0.4772.

Therefore, 0.4772 left from the mean and 0.4772 right from the mean makes our whole distribution. Adding both the values, we get 0.9544 which typically tells us that 95.44% of the total population comes under the IQ of 70–130. Cool isn’t it?

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