test 1 (part 3 )

Nominal

Categories only.
Examples:
• State
• Team
• College
• Region

Ordinal

Categories with meaningful order.
Examples:
• Poor, Average, Excellent
• No improvement, Moderate improvement, Large improvement

Interval

Equal spacing but no true zero.
Example:
• Temperature (°F, °C)

Ratio

Equal spacing plus a true zero.
Examples:
• Vertical jump height
• Recovery time
• Sales dollars
• Revenue
• Discount rates
• Sales increase

Histogram

Best for:
• Shape
• Center
• Spread
• Skewness
• Outliers

Right-Skewed

Long right tail
• Mean > Median
• High values pull distribution right

Left-Skewed

Long left tail
• Mean < Median
• Low values pull distribution left

Box-and-Whisker Plot

Best for:
• Comparing distributions
• Comparing variability
• Identifying outliers
• Comparing medians

Possible signs of improvement: Box-and-Whisker Plot

Higher median
• Entire box shifts upward

Long Upper Whisker

Suggests:
• Positive skew
• High-value outliers
• A few exceptionally large observations

Scatterplot

Best for:
Relationships between two quantitative variables.

Examples:
• Training hours vs performance
• Experience vs sales

Pie Chart

Best for:
Displaying proportions or categories.

Examples:
• Sales by state
• Athletes by college

Percentiles

The kth percentile means:

k% of observations are at or below that value.

75th Percentile

If the 75th percentile is $5,800:

• 75% of observations are ≤ $5,800
• 25% are > $5,800

80th Percentile

An observation at the 80th percentile exceeds 80% of observations

90th Percentile

90% of observations are at or below that value.

Coefficient of Variation (CV)

Used to compare consistency between groups

Lower CV (Coefficient of Variation)

More consistent
• Less relative variability

Higher CV ( Coefficient of Variation)

Less consistent
• More relative variability

When asked:
Which group is most consistent?

Look for the lowest CV.

Representative Sample

Most important requirement.
The sample should accurately represent the population.

Normality

Especially important for smaller samples and t-tests.

The population distribution should be approximately normal, or the sample size
should be large enough to support inference.