Reasoning in Psychology Using Statistics Psychology 138 Spring

Reasoning in Psychology Using Statistics Psychology 138 Spring 2017

• Exam 1 on Wednesday – In lecture: closed book, scantron – In labs: open book, open notes Annoucements Reasoning in Psychology Using Statistics

Population Sampling to make data collection manageable Inferential statistics to generalize back Sample Sampling Reasoning in Psychology Using Statistics

Where does “probability” fit in? • 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 Population Lots of Possible Samples • Examples: Odds in games of chance Inferential statistics Reasoning in Psychology Using Statistics samples n=5

What are odds of getting heads? One outcome classified as heads Total of two outcomes = 1 2 = 0. 5 Flipping a coin example: 1 flip Reasoning in Psychology Using Statistics

What are the odds of getting all heads? One 2 heads outcome Four total outcomes = 0. 25 What are the odds of getting only one heads? = 0. 50 1 Two 1 heads outcome Four total outcomes 1 Three at least one heads outcome # of heads 2 What are the odds of getting at least one heads? 0 What are the odds of getting no heads? = 0. 75 Four total outcomes One no heads outcome Four total outcomes = Flipping a coin example: 2 flips Reasoning in Psychology Using Statistics 0. 25

What are the odds of being dealt a “Royal Flush”? Prob. of A = p(A) = p(Royal Flush) = Total number of outcomes classified as A Total number of possible outcomes 4 = 0. 000001539 2, 598, 960 ~1. 5 hands out of every million hands Odds in Poker Reasoning in Psychology Using Statistics

What are the odds of being dealt a “Straight Flush”? Prob. of A = p(A) = p(straightflush) = Total number of outcomes classified as A Total number of possible outcomes 40 = 0. 00001539 2, 598, 960 ~15 hands out of every million hands Odds in Poker Reasoning in Psychology Using Statistics

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

• 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 Reasoning in Psychology Using Statistics

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. People who own dogs appear to get more exercise than those who do not … 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. Report (NY Times 2006): dog a more reliable exercise partner than a human. In the news Reasoning in Psychology Using Statistics

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. 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, 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. Shane G. Brown, Bed. and Ryan E. Rhodes Ph. D School of Physical Education, University of Victoria, British Columbia, Canada Available online 2 February 2006. American Journal of Preventive Medicine In the research literature Reasoning in Psychology Using Statistics

• Research process 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 Reasoning in Psychology Using Statistics – 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 Reasoning in Psychology Using Statistics – 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 • Research process

• Research process 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 Reasoning in Psychology Using Statistics – 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

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

• Research process – Ask research question Regimens: Pounding the – Identify variables & formulate hypothesis Pavement, Stopping at Instrument used? Fire Hydrants – Define your population Scales of measurement – Select a- research The researchers …, asking about their dog men & women, own dog or not – Nominal ownership and level of physical activity. methodology - mild, strenuous – –Ordinal Methods Collect your data from a …. Questionnaires were mailed out in 2004 to – Interval sample collect information about demographics, dog - time spent exercising – –Ratio Analyze your data ownership, leisure-time walking, physical activity levels, and theory of planned behavior – Draw conclusions based on (TPB) constructs. data – Repeat In the news Reasoning in Psychology Using Statistics

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

• Research process – Ask research question Regimens: Pounding the – Identify variables & formulate hypothesis Pavement, Causal Stopping at Claims? ? Fire Hydrants – Define population The researchers used a questionnaire to – Select research methodology interview a random sample of 351 people ages – Collect data from sample 20 to 80 in the Vancouver, British Columbia, – Research Analyze your data Which Method? ? area, The authors concede that the study… does Draw conclusions – –Observational studybased on not determine whether owning a dog itself your data – Experimental methodology makes people exercise more. – Repeat This may suggest that. . when dog owners – Quasi-experimental choose to engage in moderate physical methodology exercise, the reason may be that [the dog] is insisting on a walk. Gather 2 key pieces of data for each person: dog ownership, exercise In the news Reasoning in Psychology Using Statistics

• Research process – Ask research question Regimens: Pounding the – Identify variables & formulate hypothesis Pavement, Stopping at Fire Hydrants – Define population – Select research methodology Possible confounds? – Collect data from sample – Analyze your data If follow-up experiment were – Draw conclusions based on designed, yourwhat data would you do? – Repeat In the news Reasoning in Psychology Using Statistics

• 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 Reasoning in Psychology Using Statistics

• 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 Reasoning in Psychology Using Statistics

• Draw lettered tiles from bag – Bag contains: • A’s B’s and C’s. • Both upper and lower case letters b c a A • What’s the probability of getting an A (upper or lower case)? Prob. of A = p(A) = Total number of outcomes classified as A Total number of possible outcomes Sample space Basics of probability: Derived from games with all outcomes known Reasoning in Psychology Using Statistics C B = 2/6 = 0. 33

• What’s the probability of getting an A (upper or lower case) on the first pick and another on a second pick? a 1/6 First Pick: Prob. of A = p(A) = 2/6 = 0. 33 A + b c a A C B 2/6 1/6 Second Pick: ? – it depends on how you sample Sampling with replacement b c a A 2/6 b C B Sampling without replacement c a b C B 1/5 Basics of probability Reasoning in Psychology Using Statistics c C A B 1/5 The probabilities of selecting the titles change from 1 st to 2 nd pick

b • What’s the probability of getting an A (upper or lower case) on the first pick and another on a second pick? a A Sampling with replacement Sampling without replacement 1 st picks 2 nd picks a a A b B c C A a b a A b B c C b a A B a A b B c C B a A b c a A b B c C c a A b B C a A b B c C b B c C c C C c 36 total outcomes 4 outcomes of 2 A’s 30 total outcomes 2 outcomes of 2 A’s 4/36 = 0. 11 (2/6)*(2/6) = 0. 11 2/30 = 0. 06666 (2/6)*(1/5) = 0. 0666 1 st pick 2 nd pick 1 st pick Basics of probability Reasoning in Psychology Using Statistics 2 nd pick c C B

• 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. Starting probability of selecting a particular item 1 in 1, 000. • Sampling with replacement, odds stay at 1 in 1, 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 Reasoning in Psychology Using Statistics