PSYCHOLOGY 820 Chapters 1 3

1
PSYCHOLOGY 820Chapters 1 - 3

• Introduction
• Variables, Measurement, Scales
• Frequency Distributions and Visual Displays of
  Data

2
The Image of Statistics

• Sadistic Statistics
• How to feel about this course
• Descriptive Statistics
• Tabulating, depicting, and describing sets of
  data
• Inferential Statistics
• Generalizing from a sample to the entire
  population

HI, I'M RALPH AND I HATE STATISTICS
3
Statistics and Mathematics

• Statistics is a branch of applied mathematics
• Intuition, logical reasoning, and simple
  arithmetic are the essential tools
• Similar to studying a language
• Extensive use of the computer (SPSS)
• A word to the wise (James 122)
• Be ye doers of the word, and not hearers only,
  deceiving your own selves.

4
Case Method

• The CHAPMAN data set is from a cholesterol study
  of 200 adults who were measured on several
  variables and followed for ten years.
• The HSB data set is from the High School and
  Beyond Study achievement and demographic data
  are given for a national representative sample of
  600 high school seniors.
• The EXERCISE data set contains data on certain
  exercise and smoking variables for a forty-person
  sample.

5
Variables and Their Measurement

• Variables are non-uniform characteristics (e.g.,
  age) of observational units (e.g., persons).
• A measurement is an observation that is expressed
  as a number.
• Measurement involves assigning number to things
  according to rules.
• Measurements should be as precise and as valid as
  possible.

6
Measurement Scales

• Nominal
• Numerical naming is the most rudimentary form of
  measurement.
• Ordinal
• Achieved when a group of things can be ranked
  from low to high but has no information about the
  magnitude of the differences between the ranks.
• Interval
• The actual magnitude of the differences among the
  units is reflected in the numbers (equal
  differences in numbers correspond to equal
  differences in the amounts of the attribute
  measured). The zero point on the scale is
  arbitrary and does not represent an absence of
  the characteristic measured.
• Ratio
• Differs from interval measurement in that its
  zero point denotes the absence of the property
  measured.

7
Interrelationships Among Measurement Scales

• Level of measurement is not always
  straightforward
• The particular scale of measurement is influenced
  by the interpretation to be drawn from the data
• Exaggeration of the importance of the scale of
  measurement
• On the statistical treatment of football numbers

8
Continuous and Discrete Variables

• Continuous variables can take on any value within
  a certain range when measured such as weight,
  age, or reaction time.
• Discrete variables can take on only separated
  values when measured, such as number of children
  in a class or number of days absent.

9
Tabulating Data

• The search for order, organization, and
  lawfulness in our experience and observations
  leads to statistical summaries which can aid in
  the task of apprehending the relevant information
  in a complex data set.

10
Grouped Frequency Distributions

• To organize data into a grouped frequency
  distribution
• Find the range (max-min)
• Select the number of intervals (10-30)
• Define the score limits for the intervals
• (each interval begins with a multiple of the
  class width)
• Tally the observations into the intervals
• Count the tallies within each interval and
  express as a frequency

11
Grouping and Loss of Information

• Some information is lost when the observations
  are grouped into intervals.
• Generally, the fewer the intervals, the greater
  the loss of information.
• The grouping that best reveals or portrays the
  important features of a distribution of scores
  for the intended audience is the main
  consideration.

12
Graphing a Frequency Distribution

• The three most common methods of graphing a
  distribution are the
• Histogram (bar graph)
• Frequency (or percentage) polygon
• Ogive curve (cumulative percentage)

13
Types of Distributions
Normal
Positively skewed
Negatively skewed
Rectangular

• Bimodal

14
Percentiles

• Percentiles are points in a distribution below
  which a given percent of the cases lie.
• Percentile norms are employed for assessing
  physical grown, performance on standardized
  tests, and many other purposes.
• Percentile scores allow comparison of relative
  performance on different variables.
• Percentiles or percentile ranks are very useful
  for descriptive purposes but have serious
  drawbacks when used in statistical inference.

15
Box-And-Whisker Plots

• The box-and-whisker plot (or box plot, for short)
  is a simple and useful graph for exploring and
  summarizing an array of data.
• http//davidmlane.com/hyperstat/desc_univ.html

16
Stem-And-Leaf Displays

• Another method of portraying a set of data is the
  stem-and-leaf display which is simply a refined
  grouped frequency distribution.
• http//davidmlane.com/hyperstat/desc_univ.html

17
Time-Series Graphs

• Standard statistical figure in business and
  economics
• Useful for identifying trends and changes in
  trends in ways that other representations of data
  cannot
• The X-axis (baseline) is time
• The vertical axis is a measure of the variable of
  interest
• Extrapolated projections into the future are
  shown by the dashed line.

18
Misleading Graphs How To Lie With Statistics

• Distorted representation
• http//www.math.yorku.ca/SCS/Gallery/lie-factor.ht
  ml
• Misleading scaling and calibration
• http//www.ceri.memphis.edu/langston/CREF/lying.h
  tml
• Combination graphs