Introduction to Statistics

1
Introduction to Statistics

• Statistics Terminology
• Scales of Measurements
• Measures of Central Tendencies
• Skewness
• Measures of Variability

2
Statistics The Course

• Descriptive Statistics
• Deals with describing data that has been
  collected.

• Inferential Statistics
• Deals with data collected from samples so one can
  generalize to populations.

3
Populations vs Samples

• Population
• A population consists of all members of some
  specified group.

• Sample
• A sample is a subset of a population. It has
  the same characteristics as the population.

4
Parameters vs Statistics

• Parameters
• A measure of a characteristic of an entire
  population.

• Statistic
• A measure of a characteristic of a sample.

5
Parameters vs Statistics
In research, we obtain information about
population parameters by using information from
samples that represent the population. We apply
the laws of probability to the data collected
from the samples to generalize to the population..
6
Scales of MeasurementsThere are four commonly
used.

• Each scale is represented by numbers.
• Each scale carries a different set of
  information.
• Each scale is manipulated differently.

Knowing the distinctions between the scales is
important in descriptive and inferential
statistics.
7
Nominal

• Used to identify
• Used in place of a name
• No quantitative value
• Examples male 1 female 2
• social security number

8
Ordinal

• Has the nominal characteristics
• Used to indicate order (rank)
• Not interested in distance between rank/order
  only greater than or less than
• Examples First place, second place
• Strongly agree, agree, undecided, etc.

9
Interval

• Has the nominal and ordinal characteristics
• Both order and distance between have meaning
• Intervals between numbers are equal
• Examples IQ scores

10
Ratio

• Has the nominal, ordinal, and interval
  characteristics
• A value exists that measures the complete absence
  of the object measured.
• Examples Height 10 feet is twice as tall as 5
  feet.
• Weight 50 is twice as heavy as 25 .

11
Measures of Central Tendencies

• What is happening around the center of the data?
• Mean the arithmetic average
• Median the point where 50 of the data is above
  and 50 is below
• Mode occurs most frequently

12
The Mode

• Occurs most frequently
• Is the simplest of the central tendencies.
• No computation is required.
• Very unstable information about the data
• Only average that can be used with nominal data.

13
The Median

• The point where 50 of the data is above and 50
  is below
• Data is sorted and middle point is found.
• Is not sensitive to extreme scores.
• It is not appropriate to average median scores.

14
The Mean

• The arithmetic average
• Add the values (data) and divide by the number of
  values
• Takes into account the value of every data point.
  
• Is considered the most stable central tendency.

15
Measures of Variability

• Value describes the distribution of the data.
• Examples
• Range
• Standard Deviation

16
The Range

• Simplest measure of variability
• (Highest value minus the lowest value) plus 1
• Unreliable because it is based on only two values
  

17
The Standard Deviation

• Very useful measure of variability
• Shows the difference between a raw score and the
  mean of a set of data.
• Includes all data in the computation.

18
Skewness

• Describes visually the distribution of the data.
• Examples
• Symmetrical distribution two halves of data are
  mirror images.
• Skewed distribution Data is pulled by extreme
  scores to the left or right.

19
Symmetrical Distribution
20
Skewed DistributionsHint The tail points to the
skew.
Negatively Skewed Median right of mean More
higher scores
Positively Skewed Median left of mean More lower
scores