Slide 1Chapter 7 – Data EthicsChapter 7 – Data EthicsChapter 8 – Measuring Chapter 9 – Do numbers make sense?Slide 5Slide 6Chapter 12 – Describing Distribution with NumbersChapter 12 – Describing Distribution with NumbersChapter 13 – Normal DistributionChapter 13 – Normal DistributionEXAM 2 ReviewChapter 7 – Data Ethics•Institutional Review Board•Reviews studies to protect subjects from possible harm•Does NOT decide whether study produces valuable information•At least five (5) members•Scientist, non-scientist, one unaffiliated•Diverse (race, gender, culture)•Informed consent before data collected•Informed IN ADVANCE of any risk of harm•Usually in writing•Confidentiality (no individual data, only summaries)•Anonymity (subjects’ names not known – makes follow-up difficult•World Medical Organization: “interests of subject must prevail”•Placebo controversies exist•Behavioral and Social Science Studies have different criteria…Chapter 7 – Data Ethics•Clinical Trials:•Phase 1 – small group (20-80), evaluate safety, determine safe dosage (less about side effects than other phases since such a small group)•Phase 2 – larger group (100-300), evaluate effectiveness, further evaluate safety•Phase 3 – large groups (1,000-3,000), confirm effectiveness, monitor side effects, compare to existing treatments, other information collection•Phase 4 – post marketing studies, delineate additional information (risks, benefits, optimal use)•More stringent testing needed?•Vioxx pulled from market due to post marketing releaseChapter 8 – MeasuringChapter 9 – Do numbers make sense?•Identify variable, instrument, unit of measure, example of measure•Valid measure of a property – how a rate can be more valid measure than a count (in some cases)•Predictive validity – measure can be used to predict success on tasks related to property measured (do SAT scores have predictive validity?)•Bias – systematically overstates or understates true value•Reduce bias by getting a better instrument•Reliability – result is repeatable (random error is small)•Increase reliability by averaging several measurements (instead of just one)•Scrutinize truthfulness/correctness of data/claims•Percent change = (current – previous)/previous x 100•Positive result  “percent increase”•Negative result  “percent decrease” (can’t have > 100% decrease…)Chapter 10 – GraphicsChapter 11 – Displaying Distributions with Graphs•Types of variables:•Categorical – Nominal (categories, not ordered) / Ordinal (categories, ordered)•Quantitative – Discrete (countable) / Continuous (can be measured)•Distribution of a variable: all values and frequencies/probabilities of those values•Qualities of a good graphical display•Clearly labeled, but not over-labeled•Frequency (counts) versus Relative frequency (proportions or percentages)•Types of Graphical Displays (and when they are appropriate)•Pie Chart – (usually categorical, not ordered)•Bar Graph – (categorical or quantitative), frequency or relative frequency, bars DO NOT touch•Pictograms – can be misleading (just don’t…)•Line graph – quantitative, display change over time, time on horizontalChapter 10 – GraphicsChapter 11 – Displaying Distributions with Graphs•Types of Graphical Displays (and when they are appropriate)•Histogram – frequency or relative frequency, quantitative variables, careful when choosing how to group values (equal width, all values), bars touch•Stemplot – similar to histogram, but individual values maintained•Overall pattern of distribution•Shape (symmetric or skewed)•Center•SpreadChapter 12 – Describing Distribution with Numbers•Median – midpoint of distribution (half at or lower / half at or higher)•Know how to calculate for even number of records or odd number of records•5-number summary •Minimum•Q1 (median of data below the distribution median)•Median (Q2)•Q3 (median of data above the distribution median)•Maximum•Interquartile range = Q3 – Q1•Range = Maximum – Minimum•Outliers: < Q1 – 1.5(IQR) or > Q3 + 1.5(IQR)•Boxplots and how to interpret•Mode – most frequently occurring value•Categorical or quantitative•No mode or multiple modes (bi-modal, tri-modal, etc.)Chapter 12 – Describing Distribution with Numbers•Mean – arithmetic average ( x )•Strongly affected by extreme values•Standard Deviation ( s )•Average deviation of observations from the mean•Reported only with the mean•Data more spread out  larger standard deviation•s = 0 ONLY if there is no spread or variability in the data•You WILL NOT have to calculate the standard deviation•Mean versus Median•Remember  Mean strongly affected by extreme values•Remember  Median is NOT strongly affected by extreme values•Symmetric data  MEAN and STANDARD DEVIATION•Skewed data (left or right)  MEDIAN and 5-NUMBER SUMMARY•ALWAYS look at graphical and numeric summariesChapter 13 – Normal Distribution•Density Curve: area under the curve ALWAYS equals 1•Mean is “balancing point”•Median is “equal areas point”•Symmetric curve:•Mean = Median•Both at center of the curve•Skewed curve:•Mean pulled away from the median in the direction of the “tail”•Right skewed (affected by high values), mean > median•Left skewed (affected by low values), mean < medianChapter 13 – Normal Distribution•Normal Distribution•Centered at the mean/median•Spread controlled by the standard deviation•If standard deviation is small  bell-shape is narrow and tall•If standard deviation is large  bell-shape is wide and flatter•68 / 95 / 99.7 (Empirical) Rule•68% (0.65) data within one (1) standard deviation of the mean•95% (0.95) data within two (2) standard deviations of the mean•99.7 (0.997) data within three (3) standard deviations of the mean•Know how to compute probabilities•Know how to compute and interpret standard scores (z-scores)•Percentiles: proportion of a distribution below a given