Sathyendran S A

Technique 2.1: Sum In a word sum means the total. To calculate it we just add up all of the numbers. For the data set there are a total of 7 participants. Althouh it is rarely analysed issue, it is used to calculate other statistics. Technique 2.2: Mean It is the average of all of the numbers. To calculate mean we just calculate sum first and divide by total sample size. In math-speak: (x1+x2+…+xn)/n. Often notated as (Σxn)/n For our example: in our example mean age: 21.85 and mean monthly expenditure is 4314.29 Technique 2.3: Median Simply saying, when all of the numbers are arranged in increasing/decreasing order median is the middle number. To calculate it lets put numbers in order from least to greatest, and find the middle number. If we have an even-sized sample the median is the mean of the two middle numbers. For our example, median age: 21, median year: 2 and median monthly expenditure is 4300. Technique 2.4: Range It is the spread between the smallest and largest number in the sample. To calculate it let find the smallest and largest numbers. Subtract the smallest from the largest to get the range. For our example: Range for age: 26-19 = 7; year range: 4-1=3 and range for monthly expenditure is-=2700. Technique 2.5: Variance Page 7 of 15 Varience is the measure of the variation in the sample. It answers the question of how the variables are spread. In other way, how far does each number vary from the mean? In math-speak: Σ(x – M)2/(n-1). To get, it is recommended to use Excel to calculate this for you. In our example: Age:-; Year:-; and monthly expenditure:- Technique 2.6: Standard deviation Stardard deviation is one of the most commonly used and popular measure of how are individual numbers are spread out from the median. To calculate standard deviation lets compute the square root of the variance or use Excel to calculate it for you. In our example: Age:-; Year:-; and monthly expenditure:- Data Analysis Technique 3: Correlations Correlations are used when you want to know about the relationship between two variables. For example, you want to know consumers‟ willingness to pay and their ratings for the product quality. If the correlation is 1, meaning the willingness to pay and the ratings for the product quality are completely positively correlated and if the correlation is 0, meaning there is no correlation between these two variables. If the correlation is -1, it shows they are completely negatively correlated, meaning the higher one variable, the lower the other variable. If the absolute value of the variables is bigger than 0.5, they are usually significant. An important thing to remember when using correlations is that a correlation does not explain causation. A correlation merely indicates that a relationship or pattern exists, but it does not mean that one variable is the cause of the other. Page 8 of 15 Data Analysis Technique 4: Analysis of Variance An analysis of variance (ANOVA) is used to determine whether the difference in means (averages) for two groups is statistically significant. For example, an analysis of variance will help you determine if the high school grades of those students who participated in the summer program are significantly different from the grades of students who did not participate in the program. Data Analysis Technique 5: Linear Regressions Regression is a more accurate way to test the relationship between the variables compared with correlations since it shows the goodness of fit (Adjusted R Square) and the statistical testing for the variables. The formulas for one-variable regressions is y = ax + b and for multiple regressions is y = ax12 + bx2 + c. For y = ax + b, y is the dependent variable, x is the causal variable and the intercept is a, indicating the correlation between x and y. If “a” is 0.2 for example, it means when x variable increases 1 unit, y increases 0.2 units. If “a” is negative, meaning y decreases as x increases. For y = ax12 + bx2 + c, y is the dependent variable, x1 is causal variable 1 and x2 is causal variable 2. “a” is the intercept for variable 1 and “b” for variable 2. For example, if y = 0.6 x12 – 0.4 x2 + 0.23, it means when x1 increases 1 unit, y increases 0.6 units and when x2 increases 1 unit, y decreases 0.4 units. (Given the variables are statistically significant.) Like correlations, causation cannot be inferred from regression. Note that, these types of analyses generally require computer software (e.g., SPSS, SAS, STATA, and MINITAB) and a solid understanding of statistics to interpret the results. We provide basic descriptions of each method but encourage you to seek additional information and training before using these procedures above. Page 9 of 15