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Questions and Answers
What percentage of data lies within 2 standard deviations of the mean in a normal distribution?
What percentage of data lies within 2 standard deviations of the mean in a normal distribution?
In the context of Skewness, which term is used to describe asymmetry where the tail of the distribution is on the left side?
In the context of Skewness, which term is used to describe asymmetry where the tail of the distribution is on the left side?
What method can be used to remove outliers that are more than ± 2 standard deviations away from the mean?
What method can be used to remove outliers that are more than ± 2 standard deviations away from the mean?
In terms of Kurtosis, which term is used to describe a situation where the height of the distribution is relatively higher with heavy tails?
In terms of Kurtosis, which term is used to describe a situation where the height of the distribution is relatively higher with heavy tails?
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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?
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?
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What does a P-value greater than 0.05 indicate about the data when testing for normality using statistical methods?
What does a P-value greater than 0.05 indicate about the data when testing for normality using statistical methods?
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What is the shape of the normal distribution density curve?
What is the shape of the normal distribution density curve?
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What does the standard deviation (SD) measure in a normal distribution?
What does the standard deviation (SD) measure in a normal distribution?
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Who is the German mathematician that the Gaussian distribution is named after?
Who is the German mathematician that the Gaussian distribution is named after?
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Which of the following is NOT true about the features of the normal distribution?
Which of the following is NOT true about the features of the normal distribution?
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What is the importance of the normal distribution in biology?
What is the importance of the normal distribution in biology?
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What is the role of the mean in the normal distribution?
What is the role of the mean in the normal distribution?
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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
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Description
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.
