2. Statistics
• Methods of organizing and analyzing
quantitative data
• Tools designed to help researcher organize
and interpret numbers derived from
measuring a trait or variable
• International language that only manipulates
numbers
• Numbers do not interpret themselves
• Meaning derived from the research design
3. Categories of Statistics
Descriptive and Inferential
Descriptive Statistics
• Summarize, organize, and reduce large
numbers of observations to a few numbers
• Describe or characterize the data
• Assigning numbers to things in order to
differentiate one thing from another
4. Inferential Statistics
• Use to make inferences or predictions from the
sample to the population
• Depend on descriptive statistics
• Estimation of population characteristics from
sample
• Experimental Designs
– True Experimental – random assignment
– Quasi Experimental – Pre-test/post-test, time series
– Single subject
6. Scales of Measurement
Nominal – Categories (sex, ethnicity, party)
Ordinal – Rank order (percentile norms)
Interval – Equal difference between #s
Ratio – Equal amounts from zero
7. Nominal Scale of Measurement
• Nominal - Name
• Categories and Classifications
• Naming of mutually exclusive categories
• People, events, phenomena
• Eye color, gender, political party, group
• No order or value implied
• Assign number for coding - arbitrary
• Numbers do not represent quantity or
degree
8. Ordinal Scale of Measurement
• Ordinal – by ranked order
• Categories rank-ordered from highest to
lowest
– Equal =
– Greater than >
– Less than <
• Ranking by grade point average, percentile,
achievement test score, social class
9. Interval Scale of Measurement
• Shares characteristics with ordinal
• Equal intervals between each category
• Equal difference between variables or
attributes being measures
• Constant unit of measurement
• Difference between 5&6 = 18&19
• Year, Centigrade, Fahrenheit
10. Ratio Scale of Measurement
• Most refined type of measurement
• Ordinal and Interval
• Numbers can be compared by ratios
• Numbers represent equal amounts from
absolute zero
• Age, dollars, time, speed, class size
• Most educational measurement – not ratio
11. Graphic Portrayals of Data
• Frequency Distribution – f
• Number of times each score was attained
• Rank order and then tally
• Show most/least occurring scores
• General Shape of Distribution
• Outliers
12. Histograms and Bar Graphs
• Graphic way of
representing
frequency
distribution
• Histogram –
frequencies rank-
ordered
• Bar Graph –
order arbitrary
14. Measures of Central Tendency
• Mean –
– arithmetic average of all scores
• Median –
– point which divides a rank-ordered distribution
into halves that have an equal number of scores
– 50% above and 50% below
• Mode – score that occurs most frequently
15. Relationships among Measures
of Central Tendency
• Normal Distribution
– Mean, median, and mode about the same
– Bell shaped symmetrical curve
– Large numbers – normal distribution
• Skewed Distribution
– Positively skewed – Most scores at low end
– Negatively skewed – Most scores at high end
– Lower numbers distributed unevenly
17. Bell Curve – Normal Distribution
Mean = Median = Mode0 100
Normal curve – theoretical distribution used to
transform data and calculate many statistics
20. Measures of Variability
• Shows how spread out the distribution of the
scores is from the mean of the distribution –
dispersion of scores
• How much, on average, does each score
differ from the mean?
• Variability measures
– Range – highest and lowest (no mean)
– Standard Deviation – numerical index indicating
average variability of scores
22. SD in Normal Distribution
-1 SD0 100
34% 34%
+1 SD
68%
+1 SD = 84th
percentile
-1 SD = 16th
percentile
50%
below the
mean
50% above
the mean
23. Box and Whisker Plot
• Use to give
picture of
variability
• Size of
rectangular box
– 25th
to 75th
percentiles
• Whiskers draw
from ends of
box to 10th
and
90th
percentiles
24. Standard Scores
• Makes it easier to analyze several
distributions if means and standard
deviations are different for each distribution
• Raw scores converted to standard scores
• Provide constant normative or relative
meaning
• Obtained from the mean and standard
deviation of the raw score distribution
25. The Z-Score
• Most basic standard score
• Mean of 0
• Standard deviation of 1
• Z-score of +1 = 84th
percentile
• Z-score of –1 = 16th
percentile
• Example – IQ tests
100 = mean
15/16 = standard deviation
27. Correlation Coefficient
• Calculated number representing the
relationships between variables
• Range from –1.00 to +1.00
• High Positive Relationship (.85 .90. 96)
• Low Positive Relationship (.15 .20 . 08)
- 1 +10
High negative High positive
28. Types of Correlation Coefficients
• See Table 7.5 – page 172
• Most common
– Pearson product-moment
• r
• Both continuous
– Spearman
• rs
• Both rank-ordered