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Basic Statistics
A Brief IntroductionAllison Titcomb, Ph.D.
ICYF, SFCR, U of A
Types of Data
Stevens Levels (Scales) of Measurement:
• Nominal (Categories)• Numbers indicate difference in kind• e.g., ethnicity, gender, id#s
• Ordinal (Ordered)• Numbers represent rank orderings;
distances are not equal (e.g., grades, rank orderings on a survey)
Stevens Levels cont.
• Interval• Equal intervals, “arbitrary” zero• Ratios have no meaning• e.g., temperature in degrees F
• Ratio• Equal intervals, absolute zero• Equal ratios are equivalent• e.g, weight, height
Other Types of Data
Qualitative (nominal and ordinal) vs. Quantitative (interval and ratio)
Discrete (finite number of values) vs. Continuous (can potentially take on any numerical value)
Dichotomous (only 2 values)
What kind of data are these?
Number of crimes in a county Religious preference Pass/Fail on a test Income other examples?
Data Reduction
Descriptive Statistics a.k.a. Summary Statistics• numbers that represent some
characteristics of the set of scores• unorganized > organized• graph, shape
More data reduction
Frequency Distributions• bar diagram/histogram
• discrete vs. continuous data• nominal level
• (ordinal data-- why don’t you graph it?)
More data reduction
• frequency distributions• interval/ratio• shapes include skewed, bimodal, j
shaped…
(See samples on board/overhead)
More data reduction
Measures of Central Tendency• describing and typifying• used for comparison• Mean (typical/average score,
sensitive to extreme scores)• Median (middlemost score)• Mode (most “common” score)
More data reduction
Measures of Variability• dispersion/degree of heterogeneity• Range• Variance (degree of variability of
individual scores)• Standard Deviation (sq. root of
variance; typical “distance” between individual scores and the mean of the sample)
More data reduction
Things that contribute to variability• natural variability (true variance,
tough to measure)• sampling error• measurement error• systematic variance• MAX MIN CON
More data reduction
Normal Curve• With large numbers, many things are
“normally distributed”• majority of individuals measured are
clustered close to the mean• symmetric; mean, median, mode at
same point; range is approx. 6 standard deviations
More data reduction
Measures of relationship• Pearson’s Product Moment Correlation,
more fondly known simply as “r”• Correlation coefficient• 2 sets of scores; question is the
relationship between the 2. Is there a relationship?
• Allows us to predict; reliability
Correlation
Describing the relationship• Direction
• positive (high w/high, low w/low)• negative (low w/high, high w/low)
• Magnitude• +1.0 vs. -1.0• low correlation, no correlation
• Draw a picture a.k.a. scatterplot• Assumption is that it is Linear
Inferential Statistics
Statistics in never having to say you’re certain; judgment/ leap/ inference; generalization
population parameters and sample statistics
based on probability (relative frequency of occurrence of an event in the “long run”)
Inferential Statistics
Errors in Statistical Reasoning• Null hyp-- no difference hypothesis
Types of Errors (See Handout)• Type I
• rejecting the null when it’s true• crying wolf/false alarm/trigger happy• in law, we don’t want to convict innocent• “controlled” by alpha level (e.g., 0.05)
Inferential Statistics
• Type II• NOT rejecting the null when it’s wrong• “nice puppy” as the wolf bites your
fingers• In medicine, we’d rather treat someone
who isn’t sick than to NOT treat someone who is (HMOs might change that)
• Beta, effect size, power of a test, alpha level
Inferential Statistics
Major types of statistical tests Don’t forget: What’s the question?
• “t test” (or “t-test statistic) two means• t for two; Gossett at Guiness Student’s t
Inferential statistics
• F test• for more than two means• a t test is a baby F test• btwn/within; Fisher an agrarian
researcher (ever heard of a split plot design?)
• interactions
Inferential Statistics
• Chi square• nominal data (e.g., democrats and
republicans; males and females)
• Correlation
Inferential Statistics
Statistical vs. Practical Significance• Cost/Benefit question-- Ask
“Compared to What”• Statistically significant other?• Significant findings do NOT eliminate
the need for replication
Inferential Statistics
p = 0.0001 vs. p = 0.01 NOT effect size
Non significant findings often do not get published-- bias in literature?