Assessing Normality

Question 1

What is the Kolmogorov-Smirnov test used for?

Answer 1

Used for large datasets (greater than or equal to 2000)

Also known as K-S Lilliefors, it is more appropriate for extremely large data sets.

Question 2

What is the Shapiro-Wilk test used for?

Answer 2

Used for small datasets (less than 2000)

Question 3

What are the rules of thumb for assessing normality using skewness and kurtosis?

Answer 3

If kurtosis and skewness are not between -2 and +2, correct the data before applying tests that assume normality. Some authors use -1 to +1 as a stricter criterion.

Question 4

What does a large ratio of skewness to its standard error indicate?

Answer 4

Indicates departure from symmetry.

Question 5

What is the Kolmogorov-Smirnov statistic known for?

Answer 5

Has very high power, especially with large sample sizes.

Question 6

What does a kurtosis value less than 0 indicate?

Answer 6

Platykurtosis (flatter distribution)

Question 7

What does a kurtosis value greater than 0 indicate?

Answer 7

Leptokurtosis (more peaked distribution)

Question 8

What is skewness?

Answer 8

The lack of symmetry in a distribution.

Question 9

What does a skewness value of zero indicate?

Answer 9

A normal distribution.

Question 10

What are the possible interpretations of negative and positive skewness?

Answer 10

• Negative skewness indicates data skewed left
• Positive skewness indicates data skewed right

Question 11

What is kurtosis a measure of?

Answer 11

Whether the data are peaked or flat relative to a normal distribution.

Question 12

How does SPSS define kurtosis?

Answer 12

SPSS computes ‘excess kurtosis’, adjusting the standard normal distribution to have kurtosis of zero.

Question 13

What does a kurtosis value of 3 indicate?

Answer 13

It indicates the kurtosis for a normal distribution.

Question 14

What does a Q-Q plot assess?

Answer 14

Determines if data sets come from populations with a common distribution.

Question 15

What indicates a normal distribution in a Q-Q plot?

Answer 15

Points clustering closely around a straight line.

Question 16

What is the difference between numerical and graphical methods for assessing normality?

Answer 16

• Numerical methods: Objective, based on statistical tests
• Graphical methods: Subjective, based on plots/charts/graphs

Question 17

What is the purpose of assessing normality?

Answer 17

To determine if data satisfy assumptions for normality in statistical tests.

Question 18

What happens if skewness and kurtosis values tend toward 0?

Answer 18

The distribution approximates a normal distribution.

Question 19

What are the key properties of the standard normal distribution?

Answer 19

• Symmetric about the mean
• Mean, median, and mode are the same
• Asymptotic behavior at extremes

Question 20

What does a P-P plot assess?

Answer 20

Plots cumulative proportions against those of the test distribution.

Question 21

What does a negative skew indicate on a Q-Q plot?

Answer 21

An upward curve.

Question 22

What does a positive skew indicate on a Q-Q plot?

Answer 22

A downward curve.

Question 23

What is the main takeaway regarding normality tests?

Answer 23

Both numerical and graphical methods require judgment to conclude normality.

Question 24

What does a leptokurtic distribution indicate?

Answer 24

More peaked than a normal distribution.

Question 25

What does a platykurtic distribution indicate?

Answer 25

Flatter than a normal distribution.

Question 26

What is the formula for skewness in univariate data?

Answer 26

Skewness = (mean - median) / standard deviation

Question 27

What is the formula for kurtosis in univariate data?

Answer 27

Kurtosis = [N(N+1) / (N-1)(N-2)(N-3)] * Σ[(xi - mean) / standard deviation]^4 - [3(N-1)^2 / (N-2)(N-3)]

Question 28

What is the primary function of the Q-Q plot?

Answer 28

To visually assess whether two data sets come from the same distribution.

Question 29

What is the significance of the area beneath the curve of the standard normal distribution?

Answer 29

Corresponds to probabilities (total area equals 1).

Question 30

What does a Detrended Q-Q plot show?

Answer 30

Differences between observed and expected values of a normal distribution.

Question 31

What is the outcome of a Q-Q plot that deviates from normality?

Answer 31

Points will not lie along the straight line.

Question 32

What is the purpose of assessing normality in biostatistics?

Answer 32

To determine if data follows a normal distribution, which is essential for many statistical tests.

Question 33

True or False: A normal distribution is characterized by a symmetric bell-shaped curve.

Answer 33

True

Question 34

What graphical method can be used to assess normality?

Answer 34

Q-Q plots (quantile-quantile plots).

Question 35

Fill in the blank: The _____ test is commonly used to test for normality.

Answer 35

Shapiro-Wilk

Question 36

What does a p-value less than 0.05 in a normality test indicate?

Answer 36

It suggests that the data significantly deviates from a normal distribution.

Question 37

Which of the following is NOT a method to assess normality? A) Histogram B) Shapiro-Wilk test C) ANOVA D) Q-Q plot

Answer 37

C) ANOVA

Question 38

What is the central limit theorem's relevance to normality?

Answer 38

It states that the distribution of sample means will approximate a normal distribution as sample size increases, regardless of the population's distribution.

Question 39

True or False: Skewness and kurtosis are measures that can indicate the normality of a dataset.

Answer 39

True

Question 40

What is skewness?

Answer 40

A measure of the asymmetry of the probability distribution of a real-valued random variable.

Question 41

What does a skewness value of 0 indicate?

Answer 41

The data is perfectly symmetrical.

Question 42

Fill in the blank: A kurtosis value greater than 3 indicates a distribution that is _____ than normal.

Answer 42

more peaked

Question 43

What is the range of values for skewness in a dataset?

Answer 43

Skewness can range from negative infinity to positive infinity.

Question 44

Why is normality important for parametric tests?

Answer 44

Many parametric tests assume that the data follows a normal distribution, affecting the validity of the results.

Question 45

True or False: Non-parametric tests do not require the assumption of normality.

Answer 45

True

Question 46

What is a common graphical representation used to visually assess normality?

Answer 46

Histogram.

Question 47

What is the implication of a right-skewed distribution?

Answer 47

It indicates that the tail on the right side is longer or fatter than the left side.

Question 48

What is the implication of a left-skewed distribution?

Answer 48

It indicates that the tail on the left side is longer or fatter than the right side.

Question 49

Fill in the blank: The _____ test is used to check for normality when sample sizes are small.

Answer 49

Shapiro-Wilk

Question 50

What does a Q-Q plot compare?

Answer 50

The quantiles of the sample data against the quantiles of a normal distribution.

Question 51

True or False: A Q-Q plot that forms a straight line indicates that the data is normally distributed.

Answer 51

True

Question 52

What does it mean if the data points deviate from the straight line in a Q-Q plot?

Answer 52

It indicates that the data may not be normally distributed.

Question 53

What is the significance of the Kolmogorov-Smirnov test in assessing normality?

Answer 53

It compares the empirical distribution function of the sample with the cumulative distribution function of a normal distribution.

Question 54

Fill in the blank: A kurtosis value of less than 3 indicates a distribution that is _____ than normal.

Answer 54

flatter

Question 55

What is the effect of a small sample size on normality tests?

Answer 55

Small sample sizes can lead to unreliable results in normality tests.

Question 56

True or False: Data transformations can help achieve normality.

Answer 56

True