Annoucements Exam 1 next Wednesday in both lecture & lab Pt 1: In lecture: closed book, scantron – bring #2 pencil & know your Univ. ID# Pt 2: In labs: open book, open notes (no collaboration though) Annoucements

Inferential statistics Where does “probability” fit in? Population Randomness in sampling leads to variability in sampling error “Randomness” in short run is unpredictable but in long run is predictable Allows predictions about likelihood of getting particular samples Lots of samples n=5 Possible Samples Inferential statistics

Basics of probability: Derived from games with all outcomes known Draw lettered tiles from bag Bag contains: A’s B’s and C’s. Both upper and lower case letters A a b B c C What’s the probability of getting an A (upper or lower case)? Total number of outcomes classified as A Prob. of A = p(A) = = ?? Total number of possible outcomes (Sample space) Basics of probability: Derived from games with all outcomes known

What’s the probability of getting an A (upper or lower case) on the first pick and another on a second pick? A a b B c C 1/6 2/6 on 1st pick + a First Pick: Prob. of A = p(A) = 2/6 = 0.33 A Second Pick: ? – it depends on how you sample Sampling with replacement Sampling without replacement The probabilities of selecting the titles change from 1st to 2nd pick A a b B c C a b B c C A b B c C 2/6 1/5 1/5 Basics of probability

What’s the probability of getting an A (upper or lower case) on the first pick and another on a second pick? A a b B c C Sampling with replacement Sampling without replacement Probability? a A b B c C 30 total outcomes 2 outcomes of 2 A’s 1st picks 2nd picks 1st picks 2nd picks a a A b B c C A a A b B c C b a A b B c C B a A b B c C c a A b B c C C a A b B c C 36 total outcomes 4 outcomes of 2 A’s Probability? Basics of probability

Most statistical procedures assume sampling with replacement For large populations it turns out not to matter much Example? Sampling with replacement can also be a disadvantage in experiments – Why? Basics of probability

The researchers used a questionnaire to interview a random sample of 351 people ages 20 to 80 in the Vancouver, British Columbia, area, asking about their dog ownership and level of physical activity. Dog owners walked almost twice as many minutes per week as people who did not own dogs, and the dog owners spent more time in all forms of mild and moderate physical activity. Neither the sex of the owner nor the size of the dog made a difference: men and women who owned dogs participated in increased amounts of moderate exercise compared with those who had no dog. But no statistically significant difference between the two groups was evident in the amount of strenuous exercise performed. The authors concede that the study, published in the February issue of The American Journal of Preventive Medicine, does not determine whether owning a dog itself makes people exercise more. Shane Brown, the study's lead author and a graduate student at the Behavioral Medicine Laboratory of the University of Victoria, called this "the million-dollar question." When the researchers subtracted the time spent walking the dog from total physical activity, dog owners actually walked less than their counterparts without dogs. This, the researchers say, may suggest that the dog makes the difference. When dog owners choose to engage in moderate physical exercise, the reason may be that a four-legged member of the household is insisting on a walk. Now. People who own dogs appear to get more exercise than those who do not … Report (NY Times 2006): dog a more reliable exercise partner than a human. In the news

In the news Research process Variables Variables Ask research question Identify variables & formulate hypothesis Define your population Select a research methodology Collect your data from a sample Analyze your data Draw conclusions based on your data Repeat Variables Operational level Conceptual level Regimens: Pounding the Pavement, Stopping at Fire Hydrants Variables Independent (explanatory) variables Dependent (response) variable Control variables Random variables Confound variables The researchers …, asking about their dog ownership and level of physical activity. Methods …. Questionnaires were mailed out in 2004 to collect information about demographics, dog ownership, leisure-time walking, physical activity levels, and theory of planned behavior (TPB) constructs. In the news

In the news Research process Scales of measurement Ask research question Identify variables & formulate hypothesis Define your population Select a research methodology Collect your data from a sample Analyze your data Draw conclusions based on data Repeat Regimens: Pounding the Pavement, Stopping at Fire Hydrants Instrument used? Scales of measurement Nominal Ordinal Interval Ratio The researchers …, asking about their dog ownership and level of physical activity. Methods …. Questionnaires were mailed out in 2004 to collect information about demographics, dog ownership, leisure-time walking, physical activity levels, and theory of planned behavior (TPB) constructs. In the news

In the news Research process Ask the research question Identify variables & formulate hypothesis Define population Select research methodology Collect data from sample Analyze data Draw conclusions based on data Repeat Is the sample representative? Is there bias in sample? Regimens: Pounding the Pavement, Stopping at Fire Hydrants The researchers used a questionnaire to interview a random sample of 351 people ages 20 to 80 in the Vancouver, British Columbia, area, (i.e., mailed out questionnaires) Was it simple random sampling? Stratified random sampling? Etc.? In the news

In the news Research process Causal Claims?? Which Research Method?? Ask research question Identify variables & formulate hypothesis Define population Select research methodology Collect data from sample Analyze your data Draw conclusions based on your data Repeat Regimens: Pounding the Pavement, Stopping at Fire Hydrants Causal Claims?? The researchers used a questionnaire to interview a random sample of 351 people ages 20 to 80 in the Vancouver, British Columbia, area, Which Research Method?? Observational study Experimental methodology Quasi-experimental methodology The authors concede that the study… does not determine whether owning a dog itself makes people exercise more. This may suggest that .. when dog owners choose to engage in moderate physical exercise, the reason may be that [the dog] is insisting on a walk. In the news

In the news Research process Possible confounds? Ask research question Identify variables & formulate hypothesis Define population Select research methodology Collect data from sample Analyze your data Draw conclusions based on your data Repeat Regimens: Pounding the Pavement, Stopping at Fire Hydrants Possible confounds? Threats to internal validity? If follow-up experiment were designed, what would you do? In the news

Reviewing Producing Data Scientific method Research methods Observation methods Experimental methods Quasi-experimental (see Course Packet) Pop vs. Sample Variables Types Operational definitions Measurements Continuous and discrete Scales of measurement Errors in Measurement Validity & Reliability Dartboard example Improving validity Matching design (see CP) Double-blind design (CP) Block design (CP) Sampling Sampling error Statistics and parameters Sampling Methods Probability Sampling (3 types) Non-probability Sampling (2 types) Basic probability Reviewing Producing Data