Salkind, Statistics for People Who (Think They) Hate Statistics 5th Edition
Are Your Curves Normal? Probability and Why It Counts
This chapter introduces students to the concept of probability and how understanding probability relates to statistics in (a) the odds of a particular outcome and (b) the degree of confidence one has that the outcome is “true” and not merely due to “chance.” Specifically, students will learn about the normal curve and explain distributions under the normal curve. In addition, students will be introduced to the concept of standard scores, such as a z score. The chapter ends with real-world application, summary, and chance for students to apply what they have learned.
WHAT YOU’LL LEARN ABOUT IN THIS CHAPTER
- Why understanding probability is basic to the understanding of statistics
- What the normal, or bell-shaped, curve is and what its characteristics are
- How to compute and interpret z scores
OUTLINE Chapter 8
- Why Probability?
- The normal curve provides us with a basis for understanding the probability associated with any possible outcome.
- It also is the basis for determining the degree of confidence we have in stating that a particular finding or outcome is “true.”
- The Normal Curve (a.k.a. the Bell-Shaped Curve)
- The normal curve is a visual representation of a distribution of scores that has three characteristics.
1)The mean, median, and mode are equal to one another. This means there is only one hump (i.e., unimodal) that is right in the middle.
2)The normal curve is perfectly symmetrical, not skewed to the left or right, negative or positive.
3)The normal curve is asymptotic which means the tails of the normal curve approach the horizontal axis, but never quite touch it.
- Hey, That’s Not Normal!- While not all data sets are perfectly normal, normal distributions are found in nature very frequently, and even in populations that are not normally distributed, samples from those populations are.
- More Normal Curve 101- If you divide the area under a normal curve in segments equal to the standard deviation, you find an interesting pattern in which 34.13% of the curve is within 1 standard deviation above the mean. The area between the first and standard deviation is equal to 13.59%, and the area between the second and third standard deviation is 2.15%. The same proportions are found for the segments below the mean.
- Our Favorite Standard Score: The z Score
- A z score is the number of standard deviations the raw score is from the mean
- What z Scores Represent- They represent where the raw score falls along the horizontal axis with respect to the standard deviation, but beyond that, they can be used to determine the probability of that scores existing within the data set.
- What z Scores Really Represent- When we examine the probability of an event occurring, using z Scores, we can determine how likely an even is due to chance. If the probability is very thin, it suggests some other factor may be influencing the outcome.
- Hypothesis Testing and z Scores: The First Step- When we combine what we know about research and null hypotheses with z Scores, we are able to test the null hypothesis. This is especially interesting when we find outcomes that are extremely rare.
- Using the Computer to Compute Z Scores: On page 161, the text explains how to use SPSS to compute z scores.
- Real-World Stats: The text provides a real-world example of how z scores were used with childhood obesity research.
- Summary: Once we know how likely a test score or a difference between groups is, we can compare that likelihood to what we would expect by chance and then make informed decisions.