NURS 211 Prep Video 4 Notes

Video 4 Notes: Normal Distributions, Standard Deviations, Modality, Skewness and Kurtosis Nurse Killam [YouTube] Normal Distribution (In-depth): -​ The normal distribution is a theoretical concept of how large samples of ratio or Interval level data will look once plotted. -​ Since many variables tend to have approximately normal distributions, it is one of the most important concepts in statistics. -​ The normal curve allows for probabilities to be calculated. -​ In addition, many inferential statistics require that data are distributed normally. -​ If your data is not normal be careful what statistical tests you use with it. -​ In a normal distribution, measures of central tendency including the Mean, Median, and Mode all fall at the same midline point. -​ The mean, median and mode are all equal. -​ Normal distributions share several key features. -​ They are unimodal, meaning that there is only one peak in the distribution. -​ When divided at the mean a normal distribution takes the form of a symmetrical bell-shaped curve. Standard deviation: -​ Standard deviations are used to measure how much variation exists in a distribution. -​ Low standard deviations mean values are close to the Mean, whereas high standard deviations mean that values are spread out over a large range. -​ In a normal distribution approximately 34% of scores fall between the mean and 1 standard deviation above the mean. -​ Therefore, based on it's symmetry, approximately 68% of scores fall between 1 standard deviation above and 1 standard deviation below the mean. -​ Approximately 95% of scores fall between 2 standard deviations above and 2 standard deviations below the mean. -​ Approximately 99.7% of scores fall between 3 standard deviations above and below the Mean. -​ Z scores are used to measure how many standard deviations above or below the Mean a particular score is. -​ These scores allow for comparison and probability calculations. -​ Not all samples approximate a normal curve. -​ To understand more about distributions, it is important to understand modality, symmetry and peakedness. Modality: -​ A distribution can have more than one peak. -​ The number of peaks contained in a distribution determines the modality of the distribution. -​ Most distributions are normally distributed and have only one main peak, meaning they are unimodal. -​ However, it is possible to have distributions with two or more peaks. Distributions with two peaks are bimodal. -​ Distributions with more than two peaks are multimodal. -​ Symmetry and modality are independent concepts. -​ If two halves of a distribution can be superimposed on each other where each half is a mirror image of the other, the distribution is said to be symmetrical. -​ Sometimes data are not symmetrical. Skewness: -​ If the peak is off-centre, one tail of the distribution will be longer than the other, meaning it is skewed. -​ Skewness is a measure of the symmetry of distributions. -​ Pearson's skewness coefficient provides a non-algebraic, quick estimation of symmetry. -​ Normal distributions are symmetrical and bell-shaped. In a perfect distribution, the skewness coefficient will be equal to 0, because the Mean equals the Median. -​ Positive skewness means there is a pileup of data to the left, leaving the tail pointing to the right side of the distribution. -​ The tail has been pulled in the positive direction. -​ The data is skewed to the right. -​ In this case, the Mean is to the right of the median. -​ Positive skews are more common than negative ones. -​ Negative skewness means there is a pileup of data to the right with a long tail on the left side. -​ The tail has been pulled in a negative direction. -​ In this case, the Mean is to the left of the median. Kurtosis: -​ Kurtosis is a measure of the shape of the curve. -​ It measures if the bell of the curve is normal, flat, or peaked. -​ Using Fisher's measure of Kurtosis a normal distribution would receive a coefficient of 0 and be called Mesokurtic. -​ If the calculation of excess Kurtosis results in a large positive number, the distribution is too peaked to be considered normal. This type of data is called Leptokurtic. -​ The curve is taller and skinnier than a normal distribution. -​ If the calculation of excess Kurtosis results in a negative number, it is too flat to be normal. It would be called Platykurtic. -​ The curve is shorter and fatter than a normal distribution. -​ If a distribution is skewed, there is no need to calculate kurtosis since the distribution is already not normal.