Basic Statistics

1
Basic Statistics

• A Brief Introduction
• Allison Titcomb, Ph.D.
• ICYF, SFCR, U of A

2
Types of Data

• Stevens Levels (Scales) of Measurement
• Nominal (Categories)
• Numbers indicate difference in kind
• e.g., ethnicity, gender, ids
• Ordinal (Ordered)
• Numbers represent rank orderings distances are
  not equal (e.g., grades, rank orderings on a
  survey)

3
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

4
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)

5
What kind of data are these?

• Number of crimes in a county
• Religious preference
• Pass/Fail on a test
• Income
• other examples?

6
Data Reduction

• Descriptive Statistics a.k.a. Summary Statistics
• numbers that represent some characteristics of
  the set of scores
• unorganized gt organized
• graph, shape

7
More data reduction

• Frequency Distributions
• bar diagram/histogram
• discrete vs. continuous data
• nominal level
• (ordinal data-- why dont you graph it?)

8
More data reduction

• frequency distributions
• interval/ratio
• shapes include skewed, bimodal, j shaped
• (See samples on board/overhead)

9
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)

10
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)

11
More data reduction

• Things that contribute to variability
• natural variability (true variance, tough to
  measure)
• sampling error
• measurement error
• systematic variance
• MAX MIN CON

12
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

13
More data reduction

• Measures of relationship
• Pearsons 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

14
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

15
Inferential Statistics

• Statistics in never having to say youre certain
  judgment/ leap/ inference generalization
• population parameters and sample statistics
• based on probability (relative frequency of
  occurrence of an event in the long run)

16
Inferential Statistics

• Errors in Statistical Reasoning
• Null hyp-- no difference hypothesis
• Types of Errors (See Handout)
• Type I
• rejecting the null when its true
• crying wolf/false alarm/trigger happy
• in law, we dont want to convict innocent
• controlled by alpha level (e.g., 0.05)

17
Inferential Statistics

• Type II
• NOT rejecting the null when its wrong
• nice puppy as the wolf bites your fingers
• In medicine, wed rather treat someone who isnt
  sick than to NOT treat someone who is (HMOs might
  change that)
• Beta, effect size, power of a test, alpha level

18
Inferential Statistics

• Major types of statistical tests
• Dont forget Whats the question?
• t test (or t-test statistic) two means
• t for two Gossett at Guiness Students t

19
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

20
Inferential Statistics

• Chi square
• nominal data (e.g., democrats and republicans
  males and females)
• Correlation

21
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

22
Inferential Statistics

• p 0.0001 vs. p 0.01 NOT effect size
• Non significant findings often do not get
  published-- bias in literature?