China’s Wealth Gap Problem
Traditionally China has been one of the red states. This means that China traditionally adopted the policy of communism. Hence, one would expect the income and wealth disparity in China to be limited. However, surprisingly, that is not the case. China has one of the biggest wealth disparities in the world. For instance, the top […]
How Individuals and Companies can Protect Themselves from Systemic Risks
Systemic Risks and their Impacts Business continuity planning and management is an approach that companies adopt to protect themselves from unforeseen and high impact events. In recent years, Black Swan events or low probability high impact events that no one can foresee with accuracy have become common. For instance, the collapse of the American Investment […]
The Future of Energy
Abstract The three imperatives of sufficiency, safety, and sustainability of the global energy paradigm as it exists now along with the need to transition to a new energy paradigm are the two themes that are analyzed and evaluated in this report. The fact that the existing oil based paradigm has led to wars and conflicts […]
Six Sigma – Introduction to Analyze Phase
The Six Sigma philosophy believes in statistical facts. There is no room for error and therefore there is no room for guessing or judgement. Therefore the few inputs that were guessed for being the critical ones in the earlier stages of define and measure now need to be confirmed with statistical analysis. The purpose of […]
How a typical Business Continuity Program Works ?
In the last decade or so, the threats to the working environment of companies have multiplied ranging from 9-11 type attacks, earthquakes and the spread of diseases like SARS. Further, there is the very real threat of natural and manmade disasters like these disrupting the working patterns of organizations. Hence, there is a need to […]
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.
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.
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%.
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!
Your email address will not be published. Required fields are marked *
