Psyc 2101 1st EditionExam # 2 Study GuideProbability- Probabilities range from 0 to 1.0o 0 = there is no chance of an event happeningo 1 = an event is certain to occur- Definitions:o Event: the outcome of the trial E.g. Coin-flip; heads or tails?o Independent events: multiple events where the outcome of one doesn’t influence the outcome of the other E.g. the sex of a couple’s child; first kid, boy or girl, second kid still has a 50/50 chance of being a boy or a girlo Mutually exclusive events: multi-events where the occurrence of one precludes the occurrence of others E.g. coin flip; can’t be both heads or tails, must be one or the othero Exhaustive events: a set of events representing all possible outcomes E.g. Heads or tails is the only outcomesComputing Probability• To compute the probability of an event:o Number of events / Number of exhaustive eventsAdditive rule of probability• Given a set of mutually exclusive events, the probability of the occurrence of one event or another is equal to the sum of their separate probabilitieso Example: What is the probability of rolling a 4 or a 7 with a pair of dice? P(4 or 7) = P(4) + P(7) Total outcomes of rolling a die: 36 3/36 + 6/36 = 9/36 à .25• Examples: probability of rolling a 2 or 4 or 6?o P(2 or 4 or 6) = 1/6 + 1/6 + 1/6 = 3/6 à .5Multiplicative rule of probability• The probability of the joint occurrence of two or more independent events is the product of their individual probabilities; only independent eventso Example: What is the probability of rolling a 4 and then a 7 with a pair of dice? 3/36 * 6/36 à .0033 * .1667 = .014o Example: Couple with 3 boys, what’s the probability the 4th will be a boy? P(boy + boy + boy) = .5 à 50% .5*.5*.5= .125Joint vs. conditional probability• Joint probability: the probability of the co-occurrence of 2 or more eventso If 2 events are independent, the joint probability can be found with the multiplicativerule E.g. what's the probability students over 25 are from NC– Probability= P(>25)*P(NC)– .15x*.87= .13• Conditional probability: the probability that one event will occur given that another event has already occurredo Events are no longer independent!o E.g. What’s the probability of a car accident given that the driver has been drinking?Probability with continuous variables• All of our examples have used categorical variables (e.g. sex, coin flips).• Probability is easy to discuss with categorical variableso Why à Because they’re a set numberProbability with continuous variables• When dealing with probabilities for continuous variables we are generally not interested in probabilities for specific values of X (infinite # of values)• Rather we want to know probabilities for a range of values of Xo Use the area under the curve to find probability using the “z table” E10 in text• Example: Continuous variable• Based on one study the average length of human gestation 280.6 days (40.09 weeks), with a standard deviation of 9.7 days.• What is the probability a woman would have a baby post term (past 294 days)?o Let’s use z scores to find out!o P(post term)= .084Example: Continuous variable• Z score for 294 days• Mean= 280.6• Standard deviation= 9.7• Z= (294-280.6) / 9.7à 1.38 o Z= 1.38 o Positive score= smaller portion:• 1.38 in the text E10 is .0838 à .084• Positive = Smaller portion & negative = Larger portion• All depending if you draw a graph to helpSampling & Hypothesis TestingThe Logic of Inferential Statistics- Inferential statistics allow us to test if a sample(s) are similar to a population(s)- Or inferential stats allows us to test if the relationship between 2 or more populations- We use probability theory to determine this!- Does probability for samples hold for the population? Not necessarilyThe Logic of Inferential Statistics- Null Hypothesis: Statement about population that postulates that there’s NO difference between populations- H (subscript) o = null- Alternative (Research) Hypothesis: Postulates that there IS a difference between populations- Mutually exclusive; can either be a null or alternative hypothesis- Null is false à Reject = Ho Null is true à Fail to reject = HoExamples- What are the null and alternative hypotheses?1. Is self-esteem related to health?a. DV: Health IV: Self-esteemb. Null: “there’s no relationship between self-esteem & health”c. Alternative: “ there is a relationship between self-esteem & health”2. Are sports teams wearing black uniforms penalized more often than teams not wearing black uniforms?a. DV: number of penalties IV: color of jerseyb. Null: “there’s no relationship between the number of penalties and the color of jerseys”c. Null = “there’s no relationship/difference between the (DV) and the (IV)”d. Alternative = “there is a relationship/difference between the (DV) and the (IV)3. Do people who watch lots of violent television act more aggressively than those whodo not?a. DV: amount of violent TV IV: aggressionb. Null: there’s no relationship between the amount of violent TV & aggressionc. Alternative: there is a relationship between the amount of violent TV & aggression4. Do students feel more pride in their school after the football team wins than after it loses?a. DV: pride IV: wins and losesExamples- Do we reject or fail to reject the null hypothesis?1. Sticking to a “Mediterranean” diet reduces death from chronic disease.a. Reject the nullb. There is a relationship between the risk of chronic disease and a diet specifically a Mediterranean one2. Men and woman speak the same amount of words in a day.a. Fail to reject the null b. There is no difference between men & women in their words per day/no difference in the DV & the IV3. Hospital patients on dialysis patients are more likely to be depressed than patients not on dialysis.a. Reject the nullb. There is a relationship between patients on dialysis and depression4. Training in the correct way to lift heavy objects does not reduce complaints of back paina. Fail to reject the nullb. There is no relationship between showing them the correct way or not, they will complaint regardlessErrors- Inferences we make can be wrong.- Two types of errors:o Type I: When we reject the null/Ho but the null/Ho was correct “False positive” Uses alpha as a symbolo Type II: Occurs when we fail to reject the null/Ho but the null/Ho