PSY 330: Statistical Methods Exam 1 CHAPTER 3-4

Exam 1: Chapter 3-4

Advantage of the modes

• Only measure applicable to all scales of measurement (nominal, ordinal, interval, interval, and ratio)

• Often resistant to outliers, but not necessarily

Disadvantages of the mode

• outliers can be a problem in rare cases

• not always a good representation of a norm or center

• cant do much with statistical analysis.

Advantages of the median

• Highly resistant to outliers

• Best for skewed distributions

• Applicable to three of four scales (ordinal, interval, ratio)

Disadvantages of the median

• Difficult to perform meaningful statistical operations with the median

• Unreliable estimate of the population parameter

Advantages of the mean

• The mean makes everything possible (in stats)

• It’s generally a reliable estimate of the population parameter

• Best for normal distributions

Disadvantages of the mean

• Not applicable to nominal or ordinal scales

• Vulnerable to outliers

Measures of Central Tendency

• Mode: Nominal, Ordinal, Interval, Ratio

• Median: Ordinal, Interval, Ratio

• Mean: Interval, Ratio

Measures of Variability

Range: Difference between minimum and maximum

Interquartile Range: Range of the middle 50% of the data (75th - 25th percentile)

Variance: Average squared deviation of values from the mean

Standard Deviation: Average deviation of values from the mean

Advantages of Range

• Extremely simple to compute and interpret

• Bird’s eye view of maximum spread

Disadvantage of Range

• Functionally “useless” for most statistical purposes

• Extremely vulnerable to outliers

Advantage of IQR

• Eliminates the outlier problem

Disadvantage of IQR

• Eliminates HALF the data set in the process - overcorrection

• Also not particularly useful for most statistical analysis

Advantage of Variance

• Highly useful for statistical analysis, will show up often

Disadvantages of Variance

• Difficult to interpret “squared deviation”

• Highly vulnerable to outliers

Advantage of Standard Deviation

• Equally useful to variance in statistical analysis, will show up just as often

• Easier to interpret by eliminating the “square” from the deviation

Disadvantage of Standard Deviation

• Vulnerable to outliers

Measures of Distribution Shape

• Skewness: how much does a distribution deviate from being symmetrical

• Kurtosis: how pronounced are the peaks and tails of the distribution

Zero ____ is desired, or close to it.

Zero SKEWNESS is desired, or close to it.

High positive of negative _____ often indicates a non-normal distribution

High positive of negative SKEWNESS often indicates a non-normal distribution

____ provides another initial impression to assess normality

KURTOSIS provides another initial impression to assess normality

_____ _____ is desired

Zero kurtosis is desired (adjusted “excess kurtosis”)