# P-Value in Hypothesis Test - Interpreting the Statistical Conclusion

### What is the P-Value ?

The P-Value is a statistical representation of the likelihood that the null hypothesis is true. Therefore the P-Value is the probability that the output (Y) will not change as a result of the variation that we are deliberately introducing in the input (X).

**Example:** If we have a null hypothesis that says that there is no statistically significant relationship between the efficiency of workers in the New York factory as compared to the one in Sacramento California, then the P value attaches a probability to this statement.

If we say that for testing the following hypothesis we assign a P-Value of 0.05. This means that we are saying that 95 out of a 100 times, the efficiencies will not be different. Therefore we are admitting that 5% of the times they could be different. In this case the null hypothesis will only be rejected if we prove that differences in efficiencies arise let’s say 7% of the times.

### Decide the Relevant P Value

The P-Value is an important part of the hypothesis problem. Changing the P-Values slightly can change which hypothesis is selected and which is rejected. Therefore the selection of the P-Value must be carefully done. There are different types of errors associated with choosing the wrong P Value. These errors have been described later. The management must decide which error they can afford to make before selecting the P-Value.

### Link between the P-Value and Confidence Interval

The P-Value and confidence interval are intertwined. In fact, if you have the value of one you can automatically derive the value of the other. The formula used in P value = 1 - Confidence Interval. Therefore for a P Value of 0.05, the confidence interval is 0.95 or 95%.

### What the Conclusion Does Not Mean ?

Statistical conclusions cannot be taken literally. One needs to carefully understand how to interpret them before any decisions are made which are based on them. For instance, we stated above that the null hypothesis stands true 95% of the time. Does this mean that if we were to conduct a 100 experiments right away, the null hypothesis would stand true 95 times or more? Well, not really.

Although this is what is ideally expected to happen, the entire subject of Statistics is based on the law of large numbers. This means that these conclusions can be tested for validity only after 1000’s of trials have taken place. When the numbers are sufficiently large, 95% will hold true!

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