The Purpose of Statistics (Data Analysis) Descriptive Statistics  Describe the data. Inferential Statistics  Figure out the relationships b/w variables (factors) Is the relationship significant?  Reliable? What kind is the relationship?  + or – Statistical inference: Sample  Population Attempting to draw the population information from a sample.

How Do Statistics Accomplish Such Objectives? Hypothesis testing Theory = Central Limit Theorem: Probability, Sampling Distribution, Sampling Error Various statistical models (techniques): T-test Model ANOVA Model Regression Model Discriminant Model Structural Equation Model (SEM), etc.

Hypothesis Testing We first compute the sample mean, standard deviation, which enables us to compute: Test statistic (computed value of Z, aka, Z-score) Z-score is a standardized value, which enables us to use the probability [ 0 ≤ P(x) ≤ 1 ]; Any kind of raw data ($, quantity, etc.) can be converted to the Z-score that illustrate the nice probability distribution called “Normal Distribution.” Using such probability distribution enables us to make an inference about the population.

Level of Significance ( α ) Life is full of uncertainties. Hypothesis testing may commit an error. There will be chances that one random sample may not represent the population correctly. The chance of having such an error is called the significance level. α value = α risk = 1 – Confidence Coefficient Example: If Confidence Coefficient is 95%, then α = 1 – 0.95 = 0.05 = 5%

Level of Significance (continued) What does the significance level mean?  At α = 0.05, if we collect 100 samples and conduct such hypothesis testing 100 times, we will have 95 times the same results as this sample data.  Chances are 19 out of 20 that data supports the research hypothesis. (19/20 = 95/100 = 95% confidence coefficient)

Level of Significance (continued) As said earlier, life is full of uncertainties. Uncertainties mean risk. Managers wish to control the risk. How could they do that? Set the α at 5%, then you controlled the risk at 5%, eliminating 95% of uncertainties. In other words, by having 95% of confidence (certainties), you reduced the risk to just 5%. In business, we typically use 5%. Biology, Medicine areas may go for less risk because they deal with life/death. They usually employ 0.1% α risk (99.9% sure).