Key statistical techniques
Marketing Research – Key statistical techniques
Mathematical differences, managerially important differences and statistical significance. Statistical tests are probability based analytical techniques conducted to arrive at a decision based on a hypothesis. According to DSS Research (2011), the basic theory behind statistical inferences, is the assumption or understanding that differences between numbers may be mathematically different but not relevant statistically or important managerially. Let us examine this with an example.
A retailer carries out a customer check-out time study in 10 stores with 100 customers. If the mean time spent is 2.1 minutes and in Store 2 it is 2.4 minutes, the numbers differ mathematically (by 0.3 minutes), but they are not really significant statistically. Statistical significance is relevant only if the numerical difference is large enough, not to have been caused by sampling error or chance (Reddy & Acharyulu, 2008). Managerially important differences are those where the differences are statistically high but they still may or may not be helpful in making a managerial decision. In the above example, it can still be argued that a manager may not need to enhance the service level at check-out in Store 2, since the difference is minimal. However it is to be noted that probabilistic determinations are never absolute and they cannot be. They are always measured and tested at certain confidence levels; usually at 90% or 95% confidence level. This means that if the results are significantly different at say 95% level, there is a 5% chance that the difference could be due to sampling error; thereby making it statistically irrelevant. (DSS Research, 2011).
Null and Alternative Hypothesis
Statistical hypotheses are used to determine whether a relationship found in a sample data set, can be extrapolated to the population i.e. whether it will hold true for the whole population. There are two types of hypothesis which are used. One is called the Null hypothesis and the other is the Alternative hypothesis. Most statistical analyses require that one defines the Null hypothesis – which suggests that a relationship between two variables does NOT exist i.e. there is no difference in the values. The Alternative hypothesis is exactly opposite of the Null hypothesis and assumes that the relationship DOES exist i.e. there are differences. Alternative hypothesis can however be negative or positive, based on whether one variable decreases or increases when the other is increased. However, since hypotheses are always tested at a significance level, one can use the chi-square test to measure variability and prevent errors (Blaikie, 2003).
Scatter Diagrams
Scatter Diagrams help to visualize the relationship between two distinct variables on a set of sample data. The two variables are plotted on the X and Y axis and the values are plotted. A straight line drawn through the dots separates the data points and gives us an indication of the correlation between them – whether it’s positive, negative or none.
ANOVA DataIn this example, the degrees of freedom for numerator are 1 and denominator is 19.
So F = MSA/MSE i.e. 34,276 / 4,721 = 7.26. The F (Critical) value for d.f = (1, 19) is 4.38 at 0.05 significance or 95% confidence level. Since the calculated F value (7.26) is greater than the table value (4.38), it can be concluded that the variability observed in the data is not due to chance and the Null hypothesis (which assumes that there is no variability), should be rejected.
References
Blaikie, N., (2003). Analyzing Quantitative Data: From Description to Explanation.London: Sage Publications.
DSS Research., (2011). Statistical Significance in Perspective. DSS Research, Retrieved from: http://blog.dssresearch.com/?p=111.
Reddy, N. & Acharyulu, G. V. R. K. (2008). Marketing Research.
Hyderabad: Excel Books.
