Chapter 6 Flashcards
Probability
the likelihood of an event occuring
probability (p)=specified outcome/total outcomes
probability relation w sample and population
- It’s impossible to predict exactly which scores will be obtained when you take a sample from the popualtion
- Probability allows us to determine the likelihood of getting specific samples
- If the probability of getting a specific sample is low, we can say that the sample porbably came from some other population
If a vertical line is drawn through a normal distribution…
- The line divides the ditribution into two sections: the body and the tail
- The exact location of the line can be specified by a z-score
Proportions and z scores
- Proportions are always positive, even if the corresponding z-score is negative
- A negative z-score means the tail of the distribution is on the left side and the body is on the right, and vice versa for a positive z-score
What is the role of probability in inferential statistics?
- Probability is used to predict the type of samples that are likely to be obtained from a population. Thus, probability establishes a connection between samples and populations.
- Inferential statistics rely on this connection when they use sample data as the basis for making conclusions about populations.
Typically when are proportions used, and when is probability used?
- Proportions are used to summarize previous observations
- Probability predicts future, uncertain outcomes
Probability notation
- Probability of a specific outcome is expressed with a p (for probability) followed by the specific outcome in parentheses
- Ex. probability of selecting a king from a deck of cards is written as p (king)
- Ex. probability of obtaining heads for a coin toss is written as p (heads)
Within what range can probability values fall?
- Between 0 and 1
What is random sampling?
Random sampling requires that each individual in the population has an equal chance of being selected
Random sampling is necessary for the definition of probability to be accurate
What is a simple random sample?
A sample obtained by the process of random sampling
Independent Random Sampling
- If more than one individual is being selected, the probabilities must stay constant from one selection to the next.
- The probability that you will be selected is constant and does not change even when other individuals are selected before you are.
Equal chance and equal probability=random sampling
We will always assume that this is the sampling method being used… So we will sometimes omit the word independent
Random sampling with replacement
Returning each individual back to the population before making your next selection, to keep probability constant
Random sampling without replacement
Random sampling without the requirement of constant probabilities
What is the critical value of z for a two-tailed significance test with an alpha of 0.5? Why is this value important/what does it mean?
- z= +or- 1.96
- When using inferential statistics, having a sample with z-scores above or below 1.96 would provide evidence of a treatment effect.
- The sample is an extreme value, nearly 2 standard deviations away from the average, and therefore is noticeably different from most individuals in the original population.
- If the treatment has no effect, then the sample is a very unlikely outcome. Specifically, the probability of obtaining a sample that is beyond the ±1.96 boundaries is less than 5%.
What percentage of a normal distribution does a z score of +-1.96 represent?
- The uppermost and bottom-most 5% of tails on negative and positive side
- (The extreme scores)
