12 Questions
What percentage of data lies within 2 standard deviations of the mean in a normal distribution?
95%
In the context of Skewness, which term is used to describe asymmetry where the tail of the distribution is on the left side?
Left skewed
What method can be used to remove outliers that are more than ± 2 standard deviations away from the mean?
Q-Q plot
In terms of Kurtosis, which term is used to describe a situation where the height of the distribution is relatively higher with heavy tails?
Leptokurtic
Which test is appropriate for determining whether a set of data is significantly different from a normal distribution when the sample size is between 3 to 2000?
Shapiro-Wilk test
What does a P-value greater than 0.05 indicate about the data when testing for normality using statistical methods?
Data are normally distributed
What is the shape of the normal distribution density curve?
Symmetrical
What does the standard deviation (SD) measure in a normal distribution?
Data spread
Who is the German mathematician that the Gaussian distribution is named after?
Carl Gauss
Which of the following is NOT true about the features of the normal distribution?
It has a skewed density curve
What is the importance of the normal distribution in biology?
It is the most important distribution
What is the role of the mean in the normal distribution?
Indicator of the location of the distribution
Study Notes
The Normal Distribution
- A 'bell-shaped' density curve, symmetrical and has one peak (mode)
- The probability is greatest about the mean
- Also known as the Gaussian distribution, named after Carl Gauss, a German mathematician
- The most important distribution in biology, as most biological data are normally distributed
Features of the Normal Distribution
- Determined by two parameters: the Mean and the Standard Deviation
- The Mean is an indicator of the location of the distribution
- The Standard Deviation (SD) is an indicator of the data spread
Standard Deviation (SD)
- A small SD indicates a small spread of data
- A larger SD indicates a larger spread of data
- Characteristics of the normal distribution:
- 68.2% of the data lie within 1 SD of the mean
- 95.4% of the data lie within 2 SD of the mean (95% for 1.96 SD)
- 99.8% of data lie within 3 SD of the mean
- Can be used to remove outliers for any values more than ± 2SD away from the mean
Deviation from the Normal Distribution
- Measured by two parameters: Skewness and Kurtosis
- Skewness: measures asymmetry, with right skewed or left skewed distributions
- Kurtosis: measures height/width, with leptokurtic (narrow and tall), platykurtic (wide and short), or mesokurtic (medium) distributions
Normality of Data
- Real-world data is never perfectly normally distributed, but rather "approximate"
- Statistical tests are needed to determine whether the differences are significant
- The Shapiro-Wilk test (n = 3-2000) and the Kolmogorov-Smirnov test (n > 2000) can be used to determine the probability that the data are normally distributed
Q-Q Plot
- A Quantile-Quantile Plot used to visually check for normality
- Compares the observed values to the expected values of a normal distribution
Test your knowledge on the Gaussian distribution and its specificities, including skewness, kurtosis, Q-Q plots, and tests for normality. Understand the symmetrical and 'bell-shaped' density curve, mean probability, and continuous variables.
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