Lecture 17 ARM

Question 1

Inter-Quartile Range (IQR)

Answer 1

Definition: The range of the middle half of all the observations
Less influence of outliers - more robust
More information about the shape

Calculation: QR - Q1(75th percentile - 25th percentile)

Gets rid of the outer values

Eg important when studying inequality

Eg exam question: What is interquartile range used for?
Answer: To remove things like outliers when studying a community.

Question 2

Variance 1(yap from kevin)

Answer 2

To understand how varied the data is - only used for interval/ratio - useful for normally distributed data.

Gives an indication of how far, on average, the values are from the central tendency (mean, usually).

Why do we need to know variance?
Provides a measure of variability, that takes into account the distance of each value from the mean. By squaring the deviations, variance gives more weight to larger differences - making it sensitive to outliers.

Often used in intermediate steps to get standard deviation.

Question 3

Standard deviation

Answer 3

The square root of the variance.
Measures the average distance between each data point from the mean - but expressed in the same units as the original data. This makes it more interpretable /measurable for variability. ITPROVIDESACLEARINDICATIONOFHOWMUCHTHEVALUESDEVIATEFROMTHEMEAN.

Differs from IQR-Standard deviation ISinfluenced by outliers. Weakness or strength depending on if the outliers are measurement errors or meaningful data.

Large SD: data is widely scattered
Small SD:data clustered tightly around the mean.

Question 4

Variance and Standard deviation for anthropology

Answer 4

Used in various subfields
Eg linguistics anthro - measure variability of lingustic structures
- quantify and compare variability in data - give more patterns, nuances etc

Question 5

Variance 2 (slide)

Answer 5

Defintion: Refers to the spread of dispersion of data values in a set - how much they differ from each other

Calculation: Average of squared differences from the mean

If all the data points are almost the same - variation is low. If they vary widely, variation is high (doooiiininngng)

In everyday terms: The degree of difference among observations (also called VARIABILITYor SPREAD)

Anthro - finding differences and spread, it provides more context that average / centrality measures may overlook or hide.

Question 6

Why variation matters in anthropology

Answer 6

1. Reveals complexity - shows diversity within groups, showing that populations are not homogenous
2. Cultural and individual differences - anthros study cultural complexity, eg variances in practices, beliefs
3. Avoids misleading averages - focusing only on averages can hide important differences - eg inequalities or subgroup paterns - hence it provides context

Question 7

Range

Answer 7

Definition: The simplest measure of variation - difference between the highest and lowest values in a dataset: Calculation of max value - min value
Sensitive to outliers!
Insight: Gives a quick sense of span, but does not tell us about distribution in between - can be affected by extreme values (outliers)

Question 8

Variance and sd in the sample versus in the population

Answer 8

s = sample standard deviation
sˆ2 = sample variance
o = population sd
oˆ2 = population variance

Question 9

Understanding Outliers

Answer 9

Definition: An unusual data point that lies far outside the range of the majority of the data - much higher or lower than the rest of the observation
Impact: can skew averages and distort analysis. - but also be important signals - maybe an error or a meaningful exception

Question 10

Why visualize data?

Answer 10

1. Reveal patterns: Display distribtution of data quickly (skewed, symmetric), peaks - (common values, eg unimodal, bimodal, multimodal), clusters and outliers
2. Complement numbers: Averages and SD give summary - charts show detail - eg bimodality or skews
3. Accessibility: For many people at a glance
4. Anthropological insight: Helps spot cultural or biological patters (diversity, anomalies) that merit further inquiry (interdisciplinary audiences)
5. Keep it clear: simple, direct, effective

Question 11

Histogram

Answer 11

Definition: A histogram plots a numeric variable’s distribution as a series of bars (no middle space between the bars

x-axis: data value ranges (bins , eg 0- … any number)
y-axis: frequency (count of observations in each bar/bin

Purpose: reveal SHAPE of data / distribution
- where is the data concentrated
- spread; are valyes tightly clustered or widely dispersed
- skewness: longer tail on left or right? multiple peaks? outliers?

Anthropological uses
- Eg distribution of household sizes in villages…

Question 12

Central tendency and variation in histogram

Answer 12

Central values show up as the tallest bar region (mode) - variability indicated by the width or spread of (range of bins with counts).

Question 13

Examples of histograms

Answer 13

1. Symmetric / unimodal
2. Skew left
3. Skew right
4. Uniform
5. Bimodal
6. Multimodal

Question 13

Common pitfall histograms

Answer 13

• Misreading bin ranges - each bar covers ARANGE - not a single value! (that would be a bar chart)
• Comparing histograms with different bin widths without caution (can distort perception of shape)
• Confusing histogram (numeric bins) with bar chart (categorical) - histograms are for continuous data

Question 14

Boxplots

Answer 14

Also knows as the whisker-plot - shows median, quartiles and outliers

Box: Spans over the IQRaka Q3-Q1,middle 50% of the data
Median: Line inside the box (Q2-50th percentile)
Whiskers: Extend the data from 1.5 x IQRfrom the box (not beyond 2.7 SD)
Outliers: points beyond the box plot
See illustration

Question 15

Purpose boxplot

Answer 15

Summarise distribution SHAPE and VARIABILITY in a compact form - great for comparing multiple groups side by side
- see median differences at a glance
- see IQR (box height)
- check symmetry vs skew (is median centered in box - are whisker lengths equal?)
- identify outliers - plotted as dots

Question 15

Boxplots in anthropology

Answer 15

Compare distribution across categories
- Eg nutritional status by region, income by ethnic group etc
- conveys which groups tends higher or more variable

Question 16

Common pitfalls boxplots

Answer 16

1) Confusing median with mean (mean is NOT shown)
2) Assuming whiskers = min and max values - the whiskers are only 1.5 x IQR - outliers are separate
3) Ignoring outlier points - they can important
4) Comparing boxplot heights without considering sample size - also small n can lead to misleading boxplots.

Question 17

Scatterplot

Answer 17

Definition: Plot of individual data points on two axes (x vs y) - each point is one observation with a value for variable x and variable y (eg country and income)

Purpose: Reveal ASSOCIATION/CORRELATION between two quantitative variables
- Direction: positive correlation (upward trend), negative correlation (downward trend), or no correlation (no clear trend)
- Form: Linear, curved, clustered, or outliers influencing patterns
- Strength: How tightly do points cluster around a line or trend - tight = strong, scattered = weak

Question 18

Anthropological use of scatterplots

Answer 18

examine a potential relationship - see if higher X tends to go with higher or lower Y
-Identify subgroups or anomalies

Question 19

Central tendency and variation in scatterplots

Answer 19

• No single center shown - focus on co-variation instead of a variable’s mean
• Variation: the spread of points around any trend indicates how consistent or strongly correlated the relationship is. wide scatter = high variability and thus weak correlation

Question 20

Common pitfalls scatterplots

Answer 20

• Correlation vs causation trap
• Overplotting in large datasets - too many can obscure patterns
• Ignoring non-linear patters
• Letting outliers distort perception