Lecture 8: Probability and Hypothesis Testing Flashcards
Probability
The study of likelihood and uncertainty. Most decisions we make are based on probability. The number of ways a particular outcome can occur, divided by the total number of outcomes (frequent perspective)
Hypothesis Testing
The process of determining whether a hypothesis is
supported by the results of a project
What do probabilities vary between
0 and 1
What does a probability of 0 mean, a probability of 1 mean and a probability of .5 mean
Probability of 0.0 means the event certainly will not occur
Probability of 1.0 means the event is certain to occur
Probability of 0.5 represents maximum uncertainty
Probability of getting a ‘head’ when tossing a coin
1/2
Probability of getting the number ‘2’ in a single roll of
a die
1/6
Probability of rolling an odd number in a single roll of
a die
3/6 = 1/2
The Addition rule
The probability of one outcome or another outcome occurring on a particular trials is the sum
of their individual probabilities. Also known as the or rule, because we want to know the probability of one event or another event.
Mutually exclusive
Only one of the events can occur on a single trial. E.g., a coin toss can either be heads or tails, but not both
Addition rule example
What is the probability of having either a girl or a boy when giving birth?
𝑝 𝑔𝑖𝑟𝑙 𝒐𝒓 𝑏𝑜𝑦 = 𝑝 𝑔𝑖𝑟𝑙 + 𝑝 𝑏𝑜𝑦 = .50 + .50 = 1.00
Addition rule example
What’s the probability of drawing rolling a one or a
three when rolling a single die?
𝑝 𝑜𝑛𝑒 𝒐𝒓 𝑡ℎ𝑟𝑒𝑒 = 𝑝 𝑜𝑛𝑒 + 𝑝 𝑡ℎ𝑟𝑒𝑒 = .17 + .17 = .34
The multiplication rule
The probability of a series of outcomes occurring on
successive trials is the product of their individual probabilities. Also known as the and rule, because we want to know the probability of one event and
another event.
Multiplication rule example
The probability of getting a tail on the first toss and and on the second toss
𝑝 𝑡𝑎𝑖𝑙 𝑜𝑛 𝑓𝑖𝑟𝑠𝑡 𝑡𝑜𝑠𝑠 𝑎𝑛𝑑 𝑡𝑎𝑖𝑙 𝑜𝑛 𝑠𝑒𝑐𝑜𝑛𝑑 𝑡𝑜𝑠𝑠 = 𝑝 𝑡𝑎𝑖𝑙 𝑜𝑛 𝑓𝑖𝑟𝑠𝑡 𝑡𝑜𝑠𝑠 x 𝑝 𝑡𝑎𝑖𝑙 𝑜𝑛 𝑠𝑒𝑐𝑜𝑛𝑑 𝑡𝑜𝑠s
.5*.5=.25
Multiplication rule example
What about the probability of a couple planning a family of three children would have children in the following order: Girl, girl, boy?
Each single event is .5 (1/2)
Multiply the three events
together
p = .50 X .50 X .50 = .125
Probability and the Normal Distribution
Using a z distribution, we can calculate probabilities of obtaining particular scores. First we need to transform that score into a z score.
Probability and the Normal Distribution examples
First calculate the z score
Hey Sam, you’re probably gonna have to look at the slides for this. A whole bunch of practice exercises, examples, diagrams and pictures that I couldn’t really turn into cards. By the way, you’re very very very amazing
: )
Hypothesis Testing
The process of determining whether a statement is supported by results is hypothesis testing
Null Hypothesis:
A prediction of no differences between the groups
Alternate Hypothesis:
A prediction of differences between the groups
Hypothesis testing message
Hey Sam, so the hypothesis testing stuff was kinda difficult to turn into flashcards so you’ll have to look at the slides for examples and explanations.
I will do some flashcards for the errors in hypothesis testing though.
Hope this is helping TB
: D
Type I Error in hypothesis testing
An error in hypothesis testing in which the null hypothesis is rejected when it is true. You state there is an effect, where in reality the effect does not exist
Type II Error in hypothesis testing
An error in hypothesis testing in which the null hypothesis is accepted when it is false. You state there is no effect, where in reality the effect exists
Statistical Significance and Errors
Hey again. Yeah this part was very complex and can’t really be explained with flashcards. You’ll have to look at the slides again for explanations. If you have any questions though then feel free to ask, I did this last semester so I might be able to help.
