Learning Outcomes:

• Know the concept of probability;

• Know the application of Probability and the Normal Distribution

CHAPTER 6 

PROBABILITY

• likelihood of a particular event of interest occurring

Conditional Probability

• the probability of a particular event happening if another event (or set of conditions) has also happened.

6.1 Introduction

• probability: numerical value between 0 and 1 of all the possible outcomes-

• p indicates the probability of an event occurring, p(A) for ‘A’ occurring

• can be expressed as a decimal or percentage

6.2 Probability and the Normal Distribution

Unit Normal Table

1. The body always corresponds to the larger part of the distribution whether it is on the right-hand side or the left-hand side. Similarly, the tail is always the smaller section whether it is on the right or the left.

2.  because the normal distribution is symmetrical,  the proportions on the right-hand side are the same as the corresponding proportions on the left-hand side and proportions for negative z-scores,  you must look up the corresponding proportions for the positive value of z

3. although the z-score value changes signs from one side to the other, the proportions are always positive - used only for normal distributions

6.3 Probabilities and Proportions for Scores from a Normal Distribution

• to answer probability questions about scores (X values) from a normal distribution:

1. transform the X values into z-scores

2. use the  unit normal table  to  look up the  proportions corresponding to  the z-score values

• percentile rank: percentage of individuals in the distribution who have scores that are less than or equal to the specific score

Sampling 

Population - a complete set of measurements (or individuals or objects) having some common observable characteristic

Sample - is a subset of a population

TYPES OF SAMPLING

a. Probability Sampling - subjects of the population get an equal opportunity to be selected as a representative sample.

b. Non-probability Sampling - it is not known which individual from the population will be selected as a sample.

TYPES OF NON-PROBABILITY SAMPLING

a. Judgmental Sampling - sample members are chosen only based on the researcher’s knowledge and judgment.

b. Convenience Sampling - subjects are selected because of their proximity to the researcher.

c. Snowball Sampling - used by researchers to identify potential subjects in studies where subjects are hard to locate.

d. Quota Sampling - The sample group represents certain characteristics of the population chosen by the researcher.

TYPES OF PROBABILITY SAMPLING

a. Simple Random Sampling - a completely random method of selecting subjects. e.g. Fish Bowl Technique

b. Systematic Sampling - you choose every “nth” participant from a complete list.

c. Stratified Random Sampling - involves splitting subjects into mutually exclusive groups; similar to quota sampling

d. Cluster Sampling - a random sample of these clusters is selected; there is no need to choose groups because they already exist. e.g. Rainbow Village > Red Street

*Homogeneity – similarity

*Heterogeneity – difference

*Homogeneity – W/IN groups and BET them

*Heterogeneity – BET groups and W/IN them

DEGREES OF FREEDOM

e.g. 3 combination numbers that will have a mean of 3 = 4, 2, 3 = 9/3 = 3

2, 2, 5 = 9/3 = 3  1, 3, 5 = 9/3 = 3 Uses the Standard Deviation formula

STANDARD NORMAL DISTRIBUTION

• is in the belt curve 

• has a total area that is equal to 1

• is symmetrical

• has a mean that is equal to 0

• has a standard dev. that is equal to 1

-used to compare a score to another score

-you can only compare scores by transforming them to standard normal score

SCORE – MEAN / SND = SNN

*When the 2-score becomes negative, “prop above score” will become “prop below score”

-helps to compare scores from different samples and compare different scores from the same samples

-helps calculate the proportion of the population who would score above or below your score

*To use the standard normal distribution for analyzing our data, we often transform the scores in our samples to standard normal score

Z-SCORE

• is expressed in standard deviation units

• tells us how many standard deviations above or below the mean our score is.

SAMPLING DISTRIBUTION

• When you plot sample statistics from all of your samples as a frequency histogram, you get something called the sampling distribution.

• Thus, if you plotted the sample means of many samples from one particular population, you would have plotted the sampling distribution of the mean.

• GET THE MEAN OF ALL THE SAMPLE MEAN