Hello Class, the following is an explanation of the sum of squares, variance, and standard deviation and why it is essential to understand the difference between sample statistics and population parameters.
Within the field of descriptive statistics, it is important to understand and measure the amount of variability within a set of data. Variability is helpful to understand as it provides a measure of the differences between scores, the degree to which the scores are spread out, and can assist in determining the probability of an outcome based on the scores (Gravetta et al., 2021). Within variability, there are a number of different measurements. Three important measurements to understand are sum of square (SS), variance, and standard deviation. When calculation standard deviation, it is important to first identify deviations, which are calculated by subtracting the mean of the data set from each of the individual scores. Once deviations are obtained, the next step is to square each of them to ensure all of the data is positive and the result of the summation does not equal zero, which is the case with deviations. After the squared deviations are obtained, the sum of squares is obtained by adding the squared deviation scores (Gravetta et al., 2021).
Once the SS is obtained, the next step is to identify the variance. The variance is described in the textbook as the mean of the squared deviations (Gravetta et al., 2021). To obtain this number, one needs to take the SS and divide it by the total number of scores. This score will ultimately indicate how far the data is actually spread out. In other words, a larger variance score obtained indicates data that is farther spaced. After the variance is obtained, the standard deviation can be calculated by finding the square root of the variance value. The standard deviation is important a it shows the standard distance each score is from the mean (Gravetta et al., 2021).
When obtaining these measurements, it is important to understand that there is a differences between calculating statistics from a sample vs a population. This is because calculations made from a sample can result in bias statistics, or scores that either overestimate or underestimate the population parameters. To account for this, the calculation for the variance of a sample is modified. This is done by taking the SS and dividing it by the number of independent scores, which is found by subtracting one from the total number of scores (Gravetta et al., 2021). By doing this, one can safeguard the possibility of underestimating or overestimating the population variance.
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