Exam 2: Summary Statistics

Question 1

Levels of Measurement

Answer 1

Nominal, Ordinal, Interval, Ratio

* Need to know in order to best present and analyze your data

Question 2

Nominal

Answer 2

• Ideally exhaustive and mutually exclusive categories
• Was the sentence reportedly correct or incorrectly (or no response)?
• 2 categories: Binomial aka dichotomous
• More than 2: Multinomial

Question 3

Ordinal

Answer 3

ordered categories

Question 4

Interval

Answer 4

• Equal distances between scores
• Calculate differences but not proportions
(can be discrete or continuous)

Question 5

Ratio

Answer 5

• Interval + a true zero
(can be discrete or continuous)
• Percent correct
• e.g., 50% is twice as accurate as 25% (note that this measure is bounded)

Question 6

Levels of measurement applied to hearing measurement

Answer 6

Nominal: hearing loss or normal hearing
Ordinal: degrees, mild-profound

Question 7

Descriptive Statistics

Answer 7

• Frequencies, Percentages, Proportions

• How often a phenomenon occurred
• Primary summary measure for nominal measures
• But can be used for other data types
• Across participants or behaviors
Mean, Median, and Mode

Question 8

• Measures of Central Tendency

Answer 8

• Mean (Interval, Ratio “M”)
• Median (Ordinal, Interval, Ratio, “Mdn”)
• Mode (All types)

Question 9

Measures of Variability

Answer 9

• Min, Max
• Range = Max – Min
• Interquartile range = score at 75th percentile – score at 25th percentile; Relevant if your data have extreme highs or lows

• Standard Deviation: Dispersion of scores around the mean; Colloquially: On average, how much do observations differ from mean?
SD = sqrt(variance)

• Standard Error of the Mean: How far is the sample mean likely to be from the population mean? • SE

Question 10

Tables

Answer 10

• Rule of thumb: Data that requires ≤2 columns or rows for
a table should just be presented in the text
• Arrange/group information logically
Use APA format

Question 11

Pie chart

Answer 11

use when a number adds up to 100%

Question 12

Shapes of Distributions

Answer 12

• Important for knowing:
• The best way to summarize your data
• The type of statistical test you should perform
• Some tests assume a particular distribution (e.g., “normally distributed”)

Question 13

Normal Distribution

Answer 13

• “Gaussian curve”
• Largest number of observations at the center
• Symmetric (as many below as above)
• Fewer as you get towards extreme values; 2/3 of observations will fall within 1 SD of the mean
Value

Question 14

Skewed Distribution

Answer 14

• Not symmetric
• More extreme scores in one direction
• Mean most affected by skew
• More skewed, the more the difference between mean and median
negative skew: more extreme scores on the right

Question 15

Other Distributions

Answer 15

• Distributions can have:
• Different centers
• Different variabilities
• Different kurtosis (peakedness and shape of tails)

Question 16

Standardized Scores

Answer 16

• Accounts for both average and variability of the score
• z-score = (score – M) / SD
~Resulting Mz-score = 0 and SDz-score = 1
~How many SD above or below the mean is a given score?

• Straightforward way to relate a value to a normal distribution and to other z-scores

z scores have directional information

Question 17

t distribution

Answer 17

• A t-distribution is a z-distribution that is shifted and scaled such that:
• M = 50
• SD = 10
• Typically used:
• Small sample size
• Unknown population
standard deviation

Question 18

Outliers

Answer 18

• Extremely deviant values
• Not necessarily inaccurate!

• How to identify?

• Review your experiment notes
• Plot your raw data

-Set a priori criteria based on your measure and literature-
• Trimming of reaction times is common
• e.g., more than 2.5 SD slower than the mean, and/or <200 ms
• Box and whisker plots

How to deal with them?
• NEVER EVER remove data without minimally describing:
-how and why you did
-what the impact was on the results
-how much data you’ve removed and was removal equally distributed across conditions

• Problems can arise from interpreting data with real outliers or without “outliers”