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Lecture 11

Lecture 11.docx

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University of Toronto St. George
Shawn Lehman

ANT333 Lecture #11 Basics of Experimental Design & Data Analysis We’ll Cover 3 Topics 1. Basic research design 2. Basic statistical descriptions of data 3. Basics of correlations 1). Basic Research Design Question(s)/Hypotheses  Really the ‘heart’ of any research project.  It is best when there is existing data to create a hypothesis  If you can’t state your question(s), then you’re in trouble.  For example, your question could be, “where does Dr. Lehman get his corny jokes from?”  Then, you would state two hypotheses:  H 1 jokes are plagiarized from internet.  H 2 jokes are result of his sick, twisted mind. Null Hypothesis  Statistical hypothesis that one variable has no association with another variable or set of variables.  However, when you get your results, possible that relationship in data produced by random chance.  Need to compare the results against opposite situation: corny jokes not from internet. This is your null hypothesis – the assertion that things you were testing (i.e. corny jokes and source) not related and results product of random chance events.  Key Point: Science only tests null hypotheses! Objectives  What do you hope to accomplish (besides getting an A+!)?  I really favor listing objectives or specifics aims (subunits/components of an objective) at the end of an introduction.  For example, state, “The objective of my study was to determine the source(s) for Dr. Lehman’s corny jokes.” Strategy & Rationale  Rationale – how is easy is it to read/follow  Why is your study of interest?  Is study feasible? Easy to come up with important & interesting question (e.g., is there a God?).  But, can it be done, and do you really want to do it?  Prove that Dr. Lehman is guilty of plagiarism (he gets fired, you get an A) &/or he’s sick and twisted (you can appeal his terrible grading schemes, you get an A).  Some studies heuristic – doing science just to “know” No strong applied aspects. Experimental Design  Is your study observational or experimental?  Observational studies collect data without influencing study subject(s). 1  Experimental studies have control and experimental settings that test for differences. Ideally, neither scientist (you) nor subject (me) know which is which.  Let’s just say that your “Corny Joke” study is mostly observational. Data Collection  How will you accurately and precisely measure “corniness” of Dr. Lehman’s jokes in class?  Operational Definition.  Perhaps you measure loudness and # of students who laughed after each joke.  Use some kind of noise meter & counting system.  You would, of course, not want to laugh because that would bias your sample. Data Collection & Analyses  If jokes corny, then source is key step.  You could record the jokes and then search the internet with Google for matches (H 1.  Also, ask Dr. Lehman to be assessed by trained professionals and/or have him complete a psychiatric profile (2 ).  We’ll get to analysis in a minute, but you want to discriminate between each hypothesis. Conclusions & Issues  Now you have to wrap-up your study.  Did you achieve your objectives? If not, why?  Did you find support for any of your hypotheses? If not, why?  Always good to suggest where things could be improved (e.g., brain samples from Dr. Lehman) or issues with your data (were people laughing ‘with him’ or ‘at him’?). 2. Basic Statistics Four Scales of Measurements: 1. Nominal 2. Ordinal 3. Interval 4. Ratio Nominal Measurements  Something (trait, object, etc.) with same scale value are same on some attribute. Values of the scale have no 'numeric' meaning in way that you usually think about numbers.  Example: sex (male or female).  Permissible Arithmetic Operations: Counting  Examples of Appropriate Statistics: chi square test (χ ), runs test. Ordinal Measurements  Something (trait, object, etc.) with a higher scale value have more of some attribute. Intervals between adjacent scale values are indeterminate.  Examples: dominance rank, conservation ranking.  Permissible Arithmetic Operations: scale assignments of "greater than," "equal to," or "less than.”  Examples of Appropriate Statistics: median, Spearman's Correlation (rs), Mann-Whitney U test. 2 Interval Measurements  Intervals between adjacent scale values are equal with respect attribute being measured (e.g., difference between 8 & 9 is same as difference between 76 & 77).  Example: temperature, pH.  Permissible Arithmetic Operations: addition and subtraction of scale values.  Examples of Appropriate Statistics: mean, standard deviation, Pearson's correlation (r), Student’s t-test (t). Ratio Measurements  There is a rationale zero point for scale. Ratios are equivalent (e.g., ratio of 2 to 1 is same as ratio of 8 to 4).  Example: body mass; length or distance in centimeters, inches, miles.  Permissible Arithmetic Operations: multiplication and division of scale values.  Examples of Appropriate Statistics: mean, standard deviation, Pearson's correlation (r), Student’s t-test (t). Measures of Central Tendency  These measures tap into the average distribution of a set of scores or values in the data.  Mean  Median  Mode What do you “Mean”?  The “mean” of some data is average score or value.  Mean of a population: μ=(∑X)/N  Examples: your average GPA here at UT or average height of students in this class. Problem of Being “Mean”  The main problem associated with mean value of some data is that it is sensitive to outliers & sample size.  Hides variation of data  Problem is particularly noteworthy when you sample small populations with a high % of outliers.  Example: mean height of small group of people might be affected if one was very tall OR very short. The Median  Median is simply middle value among some scores of a variable.  No standard formula for its computation.  Because mean sensitive to extreme values, median is sometimes useful and more accurate.  Rank order and choose middle value (all values from smallest to largest). The Mode  The most frequent response or value for a variable.  Multiple modes are possible: bimodal (2 modes) or multimodal (more than two modes). Measures of Dispersion  Measures of dispersion tell us about variability in the data. Very important for latter analyses. 3  Basic question: how much do values differ for a variable from the minimum to maximum, and distance among scores in between. We use: o Range o Standard Deviation Range  r = h – l where h is high and l is low  In other words, the range gives us the value between the minimum and maximum values of a variable.  Understanding this statistic is important in understanding your data, especially for
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