skewness 9/27/2012. readings chapter 2 measuring and describing variables (pollock) (pp.37-44)...
TRANSCRIPT
Readings
• Chapter 2 Measuring and Describing Variables (Pollock) (pp.37-44)
• Chapter 6. Foundations of Statistical Inference (128-133) (Pollock)
• Chapter 3 Transforming Variables (Pollock Workbook)
Homework
• Homework Due: Chapter 2 Pollock Workbook (10/2)– Question 1: A, B, C, D, E – Question 2: B, D, E (this requires a printout) – Question 3: A, B, D – Question 5: A, B, C, D – Question 7: A, B, C, D – Question 8: A, B, C
Office Hours For the Week
• When– Friday and
Monday 11-1– Tuesday 8-12– And appointment
• Santa wears blublockers
Course Learning Objectives
• Students will learn the research methods commonly used in behavioral sciences and will be able to interpret and explain empirical data.
• Students will achieve competency in conducting statistical data analysis using the SPSS software program.
The Normal/Bell Shaped curve
• Symmetrical around the mean
• It has 1 hump, it is located in the middle, so the mean, median, and mode are all the same!
Why we use the normal curve
• To determine skewness
• The Normal Distribution curve is the basis for hypothesis/significance testing
What is skewness?
• an asymmetrical distribution.
• Skewness is also a measure of symmetry,
• Most often, the median is used as a measure of central tendency when data sets are skewed.
The Mean or the Median?
• In a normal distribution, the mean is the preferred measure
• In a skewed distribution, you go with the median
A distribution is said to be skewed if the magnitude of (Skewness value/ St. Error of Skew) is greater than 2 (in absolute
value)
Baseball Salaries again
• Divide the Skewness by its standard error– .800/.427= 1.87
• This value is less than 2 so we use the mean (92 million)
• What does the positive skew value mean???
Lets Try another One (Per Capita income in the states)
• Divide the Skewness by its standard error– .817/.337= 2.42
• The value is greater than two, and the skewness value is positive
• What is the better measure and what might cause this distribution shape?
Statistical Significance
• A result is called statistically significant if it is unlikely to have occurred by chance
• You use these to establish parameters, so that you can state probability that a parameter falls within a specified range called the confidence interval (chance or not).
• Practical significance says if a variable is important or useful for real-world. Practical significance is putting statistics into words that people can use and understand.
What this Tells us
• Roughly 68% of the scores in a sample fall within one standard deviation of the mean
• Roughly 95% of the scores fall 2 standard deviations from the mean (the exact # is 1.96 s.d)
• Roughly 99% of the scores in the sample fall within three standard deviations of the mean
A Practice Example• Assuming a normal curve compute
the age (value) – For someone who is +1 s.d, from the
mean
– what number is -1 s.d. from the mean
• With this is assumption of normality, what % of cases should roughly fall within this range (+/-1 S.D.)
• What about 2 Standard Deviations, what percent should fall in this range?