Assessing Normality Flashcards
What is the Kolmogorov-Smirnov test used for?
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.
What is the Shapiro-Wilk test used for?
Used for small datasets (less than 2000)
What are the rules of thumb for assessing normality using skewness and kurtosis?
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.
What does a large ratio of skewness to its standard error indicate?
Indicates departure from symmetry.
What is the Kolmogorov-Smirnov statistic known for?
Has very high power, especially with large sample sizes.
What does a kurtosis value less than 0 indicate?
Platykurtosis (flatter distribution)
What does a kurtosis value greater than 0 indicate?
Leptokurtosis (more peaked distribution)
What is skewness?
The lack of symmetry in a distribution.
What does a skewness value of zero indicate?
A normal distribution.
What are the possible interpretations of negative and positive skewness?
- Negative skewness indicates data skewed left
- Positive skewness indicates data skewed right
What is kurtosis a measure of?
Whether the data are peaked or flat relative to a normal distribution.
How does SPSS define kurtosis?
SPSS computes ‘excess kurtosis’, adjusting the standard normal distribution to have kurtosis of zero.
What does a kurtosis value of 3 indicate?
It indicates the kurtosis for a normal distribution.
What does a Q-Q plot assess?
Determines if data sets come from populations with a common distribution.
What indicates a normal distribution in a Q-Q plot?
Points clustering closely around a straight line.
What is the difference between numerical and graphical methods for assessing normality?
- Numerical methods: Objective, based on statistical tests
- Graphical methods: Subjective, based on plots/charts/graphs
What is the purpose of assessing normality?
To determine if data satisfy assumptions for normality in statistical tests.
What happens if skewness and kurtosis values tend toward 0?
The distribution approximates a normal distribution.
What are the key properties of the standard normal distribution?
- Symmetric about the mean
- Mean, median, and mode are the same
- Asymptotic behavior at extremes
What does a P-P plot assess?
Plots cumulative proportions against those of the test distribution.
What does a negative skew indicate on a Q-Q plot?
An upward curve.
What does a positive skew indicate on a Q-Q plot?
A downward curve.
What is the main takeaway regarding normality tests?
Both numerical and graphical methods require judgment to conclude normality.
What does a leptokurtic distribution indicate?
More peaked than a normal distribution.
What does a platykurtic distribution indicate?
Flatter than a normal distribution.
What is the formula for skewness in univariate data?
Skewness = (mean - median) / standard deviation
What is the formula for kurtosis in univariate data?
Kurtosis = [N(N+1) / (N-1)(N-2)(N-3)] * Σ[(xi - mean) / standard deviation]^4 - [3(N-1)^2 / (N-2)(N-3)]
What is the primary function of the Q-Q plot?
To visually assess whether two data sets come from the same distribution.
What is the significance of the area beneath the curve of the standard normal distribution?
Corresponds to probabilities (total area equals 1).
What does a Detrended Q-Q plot show?
Differences between observed and expected values of a normal distribution.
What is the outcome of a Q-Q plot that deviates from normality?
Points will not lie along the straight line.
What is the purpose of assessing normality in biostatistics?
To determine if data follows a normal distribution, which is essential for many statistical tests.
True or False: A normal distribution is characterized by a symmetric bell-shaped curve.
True
What graphical method can be used to assess normality?
Q-Q plots (quantile-quantile plots).
Fill in the blank: The _____ test is commonly used to test for normality.
Shapiro-Wilk
What does a p-value less than 0.05 in a normality test indicate?
It suggests that the data significantly deviates from a normal distribution.
Which of the following is NOT a method to assess normality? A) Histogram B) Shapiro-Wilk test C) ANOVA D) Q-Q plot
C) ANOVA
What is the central limit theorem’s relevance to normality?
It states that the distribution of sample means will approximate a normal distribution as sample size increases, regardless of the population’s distribution.
True or False: Skewness and kurtosis are measures that can indicate the normality of a dataset.
True
What is skewness?
A measure of the asymmetry of the probability distribution of a real-valued random variable.
What does a skewness value of 0 indicate?
The data is perfectly symmetrical.
Fill in the blank: A kurtosis value greater than 3 indicates a distribution that is _____ than normal.
more peaked
What is the range of values for skewness in a dataset?
Skewness can range from negative infinity to positive infinity.
Why is normality important for parametric tests?
Many parametric tests assume that the data follows a normal distribution, affecting the validity of the results.
True or False: Non-parametric tests do not require the assumption of normality.
True
What is a common graphical representation used to visually assess normality?
Histogram.
What is the implication of a right-skewed distribution?
It indicates that the tail on the right side is longer or fatter than the left side.
What is the implication of a left-skewed distribution?
It indicates that the tail on the left side is longer or fatter than the right side.
Fill in the blank: The _____ test is used to check for normality when sample sizes are small.
Shapiro-Wilk
What does a Q-Q plot compare?
The quantiles of the sample data against the quantiles of a normal distribution.
True or False: A Q-Q plot that forms a straight line indicates that the data is normally distributed.
True
What does it mean if the data points deviate from the straight line in a Q-Q plot?
It indicates that the data may not be normally distributed.
What is the significance of the Kolmogorov-Smirnov test in assessing normality?
It compares the empirical distribution function of the sample with the cumulative distribution function of a normal distribution.
Fill in the blank: A kurtosis value of less than 3 indicates a distribution that is _____ than normal.
flatter
What is the effect of a small sample size on normality tests?
Small sample sizes can lead to unreliable results in normality tests.
True or False: Data transformations can help achieve normality.
True
