Question of the Day

1
Session 7

• Question of the Day
• Review Descriptive statistics
• Measures of Dispersion
• Lab Assignment 4 Descriptive Statistics

2
Approaches for Describing Data

• Frequency Distributions
• Measures of Central Tendencies

3
Frequency Distributions

• Understanding the SPSS Output Navigator the
  Results

4
Frequencies
5
Measures of Central Tendencies

• Tell us what is typical in the data.
• Help us to summarize the data.
• Provide a reference point for comparing groups
  within the sample.

• 3 Common MCT
• Mode
• Median
• Mean

6
The Mode

• The category in the frequency distribution which
  contains the most cases.
• The most frequently occurring event.
• Appropriate for all variables regardless of level
  of measurement.

7

• Frequencies

Statistics respondent's gender N Valid 798 Mi
ssing 14
8
(No Transcript)
9
The Median

• The point in the distribution above or below
  which 50 percent of the observations occur.
• The central point in the distribution.
• The point that cuts the distribution in half.
• Appropriate only for interval and ratio data.

10
Frequencies
11
The Mean

• The arithmetic average.
• Calculated by summing all of the values in a
  distribution and dividing by the total number of
  cases.

12

• Frequencies

13
Frequencies
14
Measures of Dispersion

• Indicate how spread out the values are in a
  distribution.
• Variability, Variance, Deviation MOD
• In combination with MCT, a more complete
  description of the data can be made.
• Not used with nominal level data.

15
Most Commonly Used MOD for Describing Analyzing
Data

• Minimum and Maximum
• Range
• Standard Deviation

16
The Standard Deviation

• Complex formula for determining a single number
  whose size indicates the spread (variability) of
  the distribution.
• should only be applied to normal distributions.
• Best utilized with large sample sizes.
• Only used with interval/ratio level data.

17
Standard Deviation

• Page 52 --Formula
• 8 steps
• All case values are used in computation
• Tells the degree the values cluster around the
  mean.
• Useful when combined with a normal distribution
  and the mean.

18
The Normal Distribution

• Mathematicians have determined what proportion of
  the normal curve falls within the various
  segments.
• 68.26 or 34.13 of the scores in the
  distribution will fall within one standard
  deviation of the mean.
• 95.44 (13.59) will fall w/in 2 SD.
• 99.76 (2.15) will fall w/in 3 SD.

19
(No Transcript)
20
Skewed Distributions Non-normal distribution

• Negatively Skewed Distribution mean, median,
  mode. Scores concentrated toward the high end of
  the distribution.
• Positively Skewed Distribution mode, median,
  mean. Scores concentrated toward the low end of
  the distribution.

21
Summary

• Nominal FD Mode
• Ordinal FD, Mode, and Range
• Interval/Ratio FD, Mean, Median, Mode, and
  Standard Deviation.

22
Z-scores

• Setting a Foundation for Bi-variate Analysis

23
What is a Z-score?

• A z-score reflects the number of standard
  deviation units that a given raw score falls from
  the mean of the normal distribution that contains
  the score.
• Z-scores make it possible for us to take any
  single (interval/ratio) score from a normal
  distribution and gain an accurate understanding
  of where it falls relative to the other scores by
  the use of percentiles.

24
What is a Percentile?

• A point on the measurement scale below which a
  specified percentage of the groups observations
  fall the 20th percentile, for instance, is the
  value that has 20 percent of the observations
  below it.

25
Calculating Z-scores

• In order to calculate a z-score you must have the
  following information
• 1) The mean of the distribution
• 2) The standard deviation for the distribution
• 3) The raw score
• The formula for calculating the z-score is Raw
  Score - Mean/SD

26
Example

• Mean 70
• SD 10
• Raw score 87

27
Using Percentiles

• By consulting a normal distribution table, we can
  locate our z-score and find the percentage of
  scores under the normal curve between the mean
  and our z-score.
• We then add or subtract (depending on the sign of
  the z-score) from 50. This will tell us the
  percentile at which this particular score falls.

28
In Class Assignment

• Analyzing Homelessness data by generating
  appropriate descriptive statistics.
• Work in teams.
• Read the instructions!!!
• Write-up your results.