Different Types of Data
• Qualitative
• Quantitative
– Nominal scale – used to count number of cases (e.g.
girls = 1, boys = 2)
– Ordinal scale – ranked – 1st, 2nd, 3rd etc.
– Interval scale – equal intervals between consecutive
values on number scale, but no zero point (e.g.
Fahrenheit vs. Celsius, IQ scale)
– Ratio scale – ratio between numbers, has zero point
(e.g. person running 10 miles is running twice as far
as someone running 5 miles)
Agenda
• ** Please turn in your notes.
• Warm Up: Please do the sheet on your
desk
• 1. Go over completed parts of packet
• 2. Correlation Coefficients
• 3. Finish Research Methods Packet
• 4. Start Statistics
• 5. Standard Deviation Practice (if time)
• HW: Read and take notes on pages 46-55
• Study for Vocabulary Quiz next class.
Interpreting Data…
• Measures of Central Tendency…
– Mean
• average
– Median
• Middle number
• If even number of numbers, take the average of
the two middle numbers
– Mode
• Occurs the most often
• Bimodal: two modes
• Multimodal: three or more modes
Graphical representations…
• Data shown in curves
– Can be normal or skewed
• Generally result is normal curve (bell shaped curve,
normal distribution)
– Mean, median, mode fall at highest point on curve.
• Skewed distributions
– Asymmetrical, most scores grouped at one end.
• Negatively skewed
• Positively skewed
Normal Distribution
Negatively Skewed Distribution
Positively Skewed Distribution
Measures of variation
• Variance tells us more…
– How much scores differ from one another and
from the mean
• Measures include
– Range
– Variance
– Standard deviation
Range
• Spread of scores in a distribution.
– Largest score minus smallest score
– For example:
Distribution 1: 32 35 36 36 37 38 40 42 42 43 43 45
Distribution 2: 32 32 33 33 33 34 34 34 34 34 35 45
Both have a range of 13, but there is a
difference in amount of variability. So…
Variance
• How spread out a distribution is.
• It is computed as the average squared
deviation of each number from its mean.
For example, for the numbers 1, 2, and 3,
the mean is 2 and the variance is:
σ2 =
In other words…
Variance…
• Step One -Find the mean of the scores.
• Step Two -Subtract the mean from every
score.
• Step three -Square the results of step two.
• Step Four -Sum the results of step three.
5 isfour
variance
• Step Five -Divide the results of Step
step
by
N-1.
• Step Six -Take the
square
of step five.
Step 6
is standard root
deviation
Standard Deviation
• Square root of the variance
• Most commonly used measure of spread
Standard Deviation
Lower case sigma means 'standard deviation'.
Capital sigma means 'the sum of'.
x bar means 'the mean'
68, 95, 99.7 rule
• 99.7% of scores fall within 3 standard
deviations of the mean (above and below)
• 95% of scores fall within 2 standard
deviations of the mean
• 68% fall within 1 standard deviation
How To Organize Data
• Frequency distribution
– Histogram
– Frequency polygon
Histogram
Frequency Polygon
Scatterplots
• Illustrate the strength and direction of
correlations graphically
• Paired X and Y scores for each subject
are plotted as single points on a graph
• Slope of a line that best fits the pattern of
points suggests the degree and direction
of the relationship between the two
variables
Different Scatterplots
•
•
•
•
•
Fig. 1: r =1
Fig. 2: r = -1
Fig. 3: r = 0
Fig. 4: r = ~0.65
See the handout
about computing
correlation
coefficients.
Inferential Statistics
• Evaluates possibility that a correlation is a
real relationship, not just chance
• Statistical significance (p) is measure of
the likelihood of the difference between
groups
• Real difference is more likely with:
– large differences between the means of
frequency distribution
– small standard deviations
– large sample
The p value and significance
• Lower the p value, the less likely results
were due to chance
• For a difference to be significant, p usually
needs to be less than 0.05