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Class Notes
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Canada
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University of Toronto Scarborough
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Psychology
(7,818)

PSYB01H3
(260)

David Naussbaum
(2)

Lecture

Department

Psychology

Course Code

PSYB01H3

Professor

David Naussbaum

Description

Quantitative Analysis
Chapter 10: Nestor & Schutt
Research Methods in Psychology
Types of Statistics
Descriptive = describe variables in a study
Inferential = estimate characteristics of a population from a random sample
Is the effect we observed due to chance alone?
Used to test hypotheses about the relationship between variables
Must consider level of measurement
Frequency Table
Shows the number of cases and/or the percentage of cases who receive each possible score on a
variable
Often precedes the formal statistical analysis
May group the values if:
There are more than 15-20/ category
It would clarify the distribution
Resulting categories:
Should be logical
Should be mutually exclusive and exhaustive
Mutually exclusive- if ppl in one category cant be in other eg male and female
Exhaustive- everyone fits into one of these categories.. There is nothing else
Bar charts
Bars separated by spaces
Good for nominal data
Histograms
Displays a frequency distribution of a quantitative variable
-quantitative analysis- have continual lines –ordinal-no gaps
Qualitative data: Categories-discontinuous, can have bars for each group bit cant draw line
graph-gaps –order doesn’t matter b/c data is nominal not ordinal
Frequency –how often a score of 1.2.3.4 for eg occur
Begin the graph of a quantitative variable at 0 on both axes
Always use bars of equal width
The two axes should be of approximately equal length
Avoid “chart junk”
-can make a non statistically difference look like it is twice as much for eg, if cut off too high
therefore need to start at 0 for both axes
-can skew how chart looks if you have for eg, a very high y axis and small x axis
-should avoid puttting too much data in the chart= chart junk- takes away from main idea..
Three key features of a distribution’s shape:
Central tendency
Variability
Skewness Skewed: distribution is not normal, therefore can’t use t-tests, f-tests ( normal parametric
statistics)
Mode (probability average)
Most frequent score
May be more than one
May fall far from the main clustering of cases in a distribution
Median (position average)
Point that divides the distribution in half
Cannot be used at the nominal level
Normal dist: mean, mode, median have same values
Range
High score – low score
Drastically influenced by one high or low score
Variance
Average squared deviation of each case from the mean
Standard Deviation
Square root of the variance
Mean (arithmetic average)
Sum numbers and divide by N
Cannot be used at the nominal level (and sometimes not at the ordinal level)
Mean vs. Median
Should consider the purpose of the statistic
Median often makes more sense if the scale is at the Ordinal level
Median is better for skewed distributions
- No median at nominal level variables
Confidence that the mean of a random sample from a population is within a certain range of the
population mean
Calculating confidence limits:-don’t need to know how to calculate
Calculate the standard error
Decide on a degree of confidence
Multiply the standard error by 1.96
Add and subtract the value in step 3 from the sample mean
>0.5 – could happen by chance.
Confidence interval- how confident you want to be that what you’ve measured is representative
of the population –if want to be more confident: need a wider range. But the broader it is you
loose precision and its not v. likely.
Can be used to estimate a population parameter from a sample statistic
Can also be used to test a hypothesis
Two of the most common hypothesis tests:
t-test F-test
T-test:
Used for comparing two group means
t = difference in group means / variance of the entire sample
Generates a statistical value
Value is compared to a critical value found in Student’s t-table
If the calculated value exceeds the critical value, the null hypothesis is rejected.
Degrees of freedom (df)
Based on the sample size
Helps determine critical value
Larger values associated with greater statistical power
One-tailed vs. two-tailed tests
One-tailed tests specify direction
Two-tailed tests are the convention
d.f=number of observations- 1
-based on sample size.
-helps determine

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