Week 2: Normal Distribution, Inference, and Confidence Intervals

Question 1

How do you create a histogram with a normal curve?

Answer 1

Use <histogram varname, frequency normal> to overlay a normal curve on the histogram.

Question 2

What is skewness?

Answer 2

Skewness measures the symmetry of the distribution.
- Negative skew: Long tail to the left
- Positive skew: Long tail to the right
- Normal distribution: Skewness = 0

Question 3

What is kurtosis, and how is it interpreted?

Answer 3

• Kurtosis measures the “peakedness” of a distribution.
• Kurtosis = 3: Normal (mesokurtic)
• Kurtosis > 3: Leptokurtic (peaked with heavy tails)
• Kurtosis < 3: Platykurtic (flat with light tails)
  The “excess” kurtosis is used in statistics to compare the kurtosis coefficient with that of a normal distribution.
  Note: Kurtosis is often not reported in publications.

Question 4

What command shows detailed statistics, including skewness and kurtosis?

Answer 4

Use <sum varname, detail>

Question 5

What is the purpose of transforming variables?

Answer 5

To make non-normal data more normally distributed, enabling the use of parametric tests.

Question 6

How do you create a logarithmic transformation?

Answer 6

Use <generate newvar=log(varname)>
Note: You can also use the command <ln> instead of <log>. You also cannot calculate the log of a negative number (or zero). These numbers, if present, will be set to system-missing in the transformed variable.</log></ln>

Question 7

What are Z-scores, and why are they useful?

Answer 7

Z-scores standardise data, converting it to a distribution with a mean of 0 and SD of 1, useful for comparison across datasets.

Question 8

How do you create Z-scores?

Answer 8

Use <egen zvarname = std(varname)>
These are more useful for more advanced statistics, such as regression.

Question 9

How do you perform analysis on specific sub-groups?

Answer 9

Use the <if> condition, e.g., <sum varname if groupvar == value></if>

Question 10

Differentiate between = and ==

Answer 10

”=” assigns values e.g., <generate>
"==" tests for equality e.g., if var == 10</generate>

Question 11

What is routing in survey data?

Answer 11

Routing directs respondents to specific questions based on prior responses, often resulting in linked variables.

Question 12

How do you check for routing?

Answer 12

Use <tab> to examine linked variables.</tab>

Question 13

What does command <tab1> do?</tab1>

Answer 13

It generates frequency tables for multiple variables at once. Example <tab1></tab1>

Question 14

How do you calculate CIs for the mean?

Answer 14

Use <ci></ci>

Question 15

What affects the width of a CI?

Answer 15

• Higher confidence levels widen the interval
• Larger sample sizes narrow the interval
• Increased variability (SE) widens the interval

Question 16

What is the significance of overlapping CIs?

Answer 16

If intervals overlap, differences between groups are unlikely to be statistically significant.

Question 17

How do you explore relationships between multiple categories?

Answer 17

Use <bysort categoryvar: sum varname> or <bysort categoryvar: tab var1 var2>

Question 18

How do transformations like logarithm and square root affect skewed data?

Answer 18

They reduce skewness and bring the distribution closer to normality, especially for positively skewed data.
Square root transformations are often used for count data (e.g., counting the number of butterflies seen in a garden each day), when low counts might be more common than higher counts.

Question 19

What are examples of linked variables in the ELSA dataset?

Answer 19

• heill (long-term illness) and helim (activity limitation)
• spcaa (caring responsibilities) and spcac (hours spent caring)

Question 20

How do you check skewness and kurtosis for a variable?

Answer 20

Use <sum varname, detail>

Question 21

How do you interpret a mean with 95% CIs?

Answer 21

The interval represents the range in which the true population mean is likely to fall, within 95% confidence.

Question 22

What are graphical ways of assessing normality?

Answer 22

Histogram, boxplot, a probability-probability (P-P) plot, and a quantile-quantile (Q-Q) plot.

Question 23

What are numerical ways of assessing normality?

Answer 23

Kolmogorov-Smirnov test, Shapiro-Wilk test, and the Skewness/Kurtosis tests.

Question 24

What is a way to show label and values aside from using <tab>?</tab>

Answer 24

Command <fre>
It is user-written so it has to be installed first through using the command <ssc>
To view the labels and values of a variable, simply use <fre></fre></ssc></fre>

Question 25

What is a smoother alternative to using histograms to assess normality?

Answer 25

Kernal density plots - approximate the probability density of a variable.
Unlike histograms, Kernal density plots are not sensitive to the number and positioning of bins used in the display.

Question 26

How do you do simple calculations?

Answer 26

Use command <display> followed by calculation</display>