Class notes Chapter 6 STATS-2126 Essentials of Statistics for the Behavioral Sciences, ISBN: 9780357035580
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PSYC-2606 (STATS2126)
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Laurentian University (LU
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Statistics for the Behavioral Sciences
Lecture notes study book Essentials of Statistics for the Behavioral Sciences of Frederick J Gravetter, Larry B. Wallnau, Lori-Ann B. Forzano, James E. Witnauer (Chapter 6) - ISBN: 9780357035580 (chapter 6)
Class notes Chapter 5 Statistics (STATS-2126) Essentials of Statistics for the Behavioral Sciences, ISBN: 9780357035580
Class notes Chapter 4 STATS-2126 Essentials of Statistics for the Behavioral Sciences, ISBN: 9780357035580
Class notes Chapter 3 STATS-2126 Essentials of Statistics for the Behavioral Sciences, ISBN: 9780357035580
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1 of 17 Wednesday, November 4, 2020
Chapter 6 - Probability
6-1 Introduction to Probability
The role of inferential stats is to use the sample data as the basis for answering questions
about the population. To accomplish this goals, inferential procedures are typically built around
the concept of probability. Speci cally, the relationships between samples and populations are
usually de ned in terms of probability.
- You begin with a population and then use probability to desire the sample that could be
obtained.
• Working backwards
1. Build probability bridge from population to samples
• Identifying the types of samples that probably can be obtained rom speci c
populations.
2. Reserve
Defining Probability
For a situation when several di erent outcomes are possible, the probability for any speci c
outcome is de ned as a fraction or a proportion of all the possible outcomes. If the possible
outcomes are identi ed as A, B, C, D…etc, then
Note:
Typically proportion # of outcomes classi ed as A
is used to Probability of A =
summarize previous Total # of possible outcomes
observations and
probability is used
to predict future,
uncertain
outcomes.
Probability Propportion
“What is the probability of selecting a king from a “What proportion of the whole deck of cards
normal deck of cards?” consists of kings?”
Sample: There are 4 kinds in a normal deck of cards
population: There are 52 cards in a normal deck
4 4
p= p=
53 53
4
Both probability and proportion are p = or 4 out of 52
53
fi fi fi ff fi fi fi fi
, 2 of 17 Wednesday, November 4, 2020
Probability Values
The de nitions we are using identi ed probability as a fraction of a proportion. I you work from
this de nition, the probability values obtained can be explained as a reaction.
For example, if you are picking a random card or ipping a coin.
13 1 1
p(spade) = = p(heads) =
52 4 2
You should notice, these fractions can be expressed equally as either percentage or decimals
13 1 1
p(spade) = = = 0.25 = 25% p(heads) = = 0.50 = 50%
52 4 2
* Probability values most often are accepted as decimal values
Note: Probability is contained within a limited range
- At one extreme, when a event never occurs, probability is 0 or 0%
- Other extreme, when an event always occurs, probability is 1 or 100%
Random Sampling
Random Sampling required that each individual in the population has an equal chance of being
selected. A sample obtained by this process is called a simple random sample.
A second requirement, necessary for many statistical formulas, statistics that have more than 1
individual being selected, the probability met stay constant from one selection to the next. This
produces independent random sampling.
- Independent referring to the fact that probability of selecting any particular individual is not
in uences by individuals already selected for the sample.
- Because independent random sampling is usually a required component for most statistical
procedures, we will always assume this is the dumpling method being used
- We will omit the word independent and refer to it simply as random sampling
• However, always assume both requirements
1. Equal chance
2. Constant probability
Independent Random Sampling requires each individual has an equal chance of being elected
and that the probability of being selected stays constant from one selection to another if more
fl fi fi fl
, 3 of 17 Wednesday, November 4, 2020
than 1 individual is selected. A sample obtained with this technique is called undefended
random sampling or simple, random sample.
Consequences of the 2 requirements
1. Equal chance
1
- Assures no bias - a population with N, each individual mist have p = of being
N
selected
- Prohibits application of probability to situations in which the possible outcomes are not
equally likely
• Ex: Winning $1 Million - either win or lose
- Because the two alternatives were not equally likely, the simple de nition of
probability does not apply.
2. Constant probability
• Ex: picking jack of diamonds from a deck of cards
1 If 1st card was not J diamonds, then
p(J diamonds) = 1
52 p(J diamonds) =
51
If 1st was J of diamonds, then
p(J diamonds) = 0
*Notice that this does not support the second requirement, so to keep probabilities from
changing from one selection to the other, it is necessary to return each individual to the
population before your next selection. This process is called sampling with Replacement.
Probability and Frequency Distribution
If you think of graphs as representing the entire population, then di erent portions of the graph
represent di erent portions of the population. Because probabilities and portions are
equivalent, a particular portion of the graph corresponds to a particular probability in the
population.
Example 6.1 (pg 183): A population of N=10 has the scores, 1, 1, 2, 3, 3, 4, 4, 4, 5, 6
If you are taking a random sample of n = 1 score from
this population, what is the probability of obtaining an
individual with a score greater than 4?
p(X>4) = ?
In relation to protection you 8
p(X<5) =
can see 2 blocks out of the 10 10
are greater than 4
ff fiff
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