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Introduction to Statistical Theory Part 1 by Prof. Sher Muhammad Chaudhry, PhD When a statistician says "statistically significant", what does it mean? In this first tutorial of the series, we will explore how to determine whether a result is statistically significant or not. The calculation used for this determination is called the p-value check. In later tutorials, we will see how other formulas can be used as well as other methods that can be made use of in order to respond critically and appropriately. The development of statistics has been a major part of science for centuries, and continues to have a profound impact on our understanding of how nature works and why things happen as they do. Statistics has been instrumental in enabling fields such as medical research, technology, business and the social sciences to make insights from data that could not be achieved with a single study. In fact, many of the modern techniques that we use in the everyday lives of consumers and businesses were first developed for other purposes. In this tutorial series, we will introduce you to these techniques and take a look at their history. Statistics is a method of investigating relationships between variables – things that vary – through comparisons between them, or inferences about those variables from observations about them. Variables might include different objects or events (e.g., heights measured for various children), different parts of the same object (e.g. the shapes of teeth), different amounts of the same thing (money), or different quantities of different things (e.g., the number of people in a group who are vaccinated). The statistical procedures used to investigate these relationships are called statistical methods. Statistical Tests Test whether data is significant, i.e., the null hypothesis that the difference between groups is due solely to chance rather than to real differences between them. Hypothesis testing is a statistical method used to determine if an observed difference between two or more groups is due solely to chance, i.e., if the differences are so extreme that they are not likely to have occurred by chance. Hypothesis testing uses the null hypothesis of "no difference" as the assumption of interest, so it is also called hypothesis testing. Parameters are variables that describe the values of objects being used for comparison, e.g., heights of students or variables being measured on a test. Statistical distributions are used to model real world data where all observations have equal probability of occurring under certain circumstances, e.g. if the number of students in a class is the same, each student will have an equal chance of being selected for participation. Statistical tests are performed to compare the null hypothesis of no difference with the alternative hypothesis that there is a difference between groups. The formula for calculation of p-value is given below: To test whether a difference between two groups is significant we make the following assumptions: 1. There is no real difference between the groups; 2. The null hypothesis, "no difference", implies that any observed difference has occurred by chance and not due to any real and significant (i.e., substantive) differences; 3. cfa1e77820