Reasoning in Psychology Using Statistics Spring 2018

Annoucements Exam 1 on Wednesday In lecture: closed book, scantron In labs: open book, open notes Annoucements

Where does “probability” fit in? Population Sample Sampling

Sampling Where does “probability” fit in? Population Possible Samples 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 Sample Sampling Examples: Odds in games of chance

Flipping a coin example: 1 flip What are odds of getting heads? One outcome classified as heads = 1 2 = 0.5 Total of two outcomes Flipping a coin example: 1 flip

Flipping a coin example: 2 flips What are the odds of getting all heads? One 2 heads outcome Four total outcomes = 0.25 # of heads 2 What are the odds of getting only one heads? Four total outcomes = 0.50 Two 1 heads outcome 1 Four total outcomes = 0.75 Three at least one heads outcome What are the odds of getting at least one heads? 1 What are the odds of getting no heads? Four total outcomes = 0.25 One no heads outcome Flipping a coin example: 2 flips

Odds in Poker What are the odds of being dealt a “Royal Flush”? Total number of possible outcomes Total number of outcomes classified as A Prob. of A = p(A) = 4 p(Royal Flush) = = 0.000001539 2,598,960 ~1.5 hands out of every million hands Odds in Poker

Odds in Poker What are the odds of being dealt a “Straight Flush”? Total number of possible outcomes Total number of outcomes classified as A Prob. of A = p(A) = 40 p(straightflush) = = 0.00001539 2,598,960 ~15 hands out of every million hands Odds in Poker

Odds in Poker What are the odds of being dealt a …? Total number of possible outcomes Total number of outcomes classified as A Prob. of A = p(A) = Odds in Poker

Reviewing Producing Data Scientific method Research methods Observation methods Experimental methods Quasi-experimental Variables Types Operational definitions Sampling Samples and populations Statistics and parameters Techniques Measurements Continuous and discrete Scales of measurement Instrument Errors in Measurement Validity & Reliability Confounds Bias Experimental control Basic probability SPSS data basics Reviewing Producing Data

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 research literature Results The analyses revealed that dog owners spent more time in mild and moderate physical activities and walked an average of 300 minutes per week compared to non–dog owners who walked an average of 168 minutes per week. A mediator analysis suggests that dog obligation acts as a mediator between dog ownership and physical activity. Moreover, the theory of planned behavior constructs of intention and perceived behavioral control explained 13% of the variance in walking behavior with an additional 11% variance in walking behavior being explained by dog obligation. Regarding intention to walk, the TPB explained 46% of the variance in intention to walk with dog obligation adding an additional 1% variance. Conclusions In this group of Canadians, those who owned a dog participated in more mild to moderate physical activity than those who did not. Acquiring a dog should be explored as an intervention to get people more physically active. Background Dog ownership may be an effective tailored intervention among adults for promoting physical activity. This study examined the relationship between walking, physical activity levels, and potential psychological mediators between people who owned dogs and those who did not own dogs in the Capital Region District of Greater Victoria, British Columbia, Canada. Data were collected in September 2004; analyses were conducted in January 2005. Methods A random sample of men (n=177) and women (n=174) aged 20 to 80 years participated. 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. Shane G. Brown, Bed. and Ryan E. Rhodes PhD School of Physical Education, University of Victoria, Victoria, British Columbia, Canada Available online 2 February 2006. American Journal of Preventive Medicine In the research literature

In the news Research process Ask research question Identify variables & formulate hypothesis Define population Select research methodology Collect data from a sample Analyze data Draw conclusions based on data Repeat Regimens: Pounding the Pavement, Stopping at Fire Hydrants People who own dogs appear to get more exercise than those who do not … In the news

In the news Research process Context for our numbers Ask research question Identify variables & formulate hypothesis Define population Select research methodology Collect data from a sample Analyze data Draw conclusions based on data Repeat Context for our numbers Regimens: Pounding the Pavement, Stopping at Fire Hydrants People who own dogs appear to get more exercise than those who do not … In the news

In the news Research process Ask research question Identify variables & formulate hypothesis Define population Select research methodology Collect data from a sample Analyze data Draw conclusions based on data Repeat Regimens: Pounding the Pavement, Stopping at Fire Hydrants People who own dogs appear to get more exercise than those who do not … 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. - men & women, own dog or not - mild, strenuous 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. - time spent exercising 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? 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 Variables Types Operational definitions Sampling Samples and populations Statistics and parameters Techniques Measurements Continuous and discrete Scales of measurement Instrument Errors in Measurement Validity & Reliability Confounds Bias Experimental control Basic probability SPSS data basics Reviewing Producing Data

The next 4 slides are Bonus material (not covered on Exam 1, only covered in lecture if it comes up and there is extra time) Sampling and probability Sampling with replacement Sampling without replacement Bonus material

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) = = 2/6 = 0.33 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 + 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 (2/6)*(1/5) = 0.0666 1st pick 2nd pick a A b B c C 30 total outcomes 2 outcomes of 2 A’s 2/30 = 0.06666 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 4/36 = 0.11 (2/6)*(2/6) = 0.11 1st pick 2nd pick Basics of probability

Most statistical procedures assume sampling with replacement For large populations it turns out not to matter much e.g., suppose your population is N=1,000,000. Starting probability of selecting a particular item 1 in 1,000,000. Sampling with replacement, odds stay at 1 in 1,000,000 Sampling without replacement, odds change to 1 in 999,999 the change is so small that it may not matter In experiments, you typically don’t want to use sampling with replacement because of the potential for lasting effects of your independent variable Basics of probability