If a particular difference is so huge that there it is not likely to have occurred due to sampling error or chance, then the difference is statistically different. It is important to note that it can never be said with absolute certainty that two given numbers are significantly different. Typically, numbers are tested at a certain level of confidence, with 95% being an average degree of confidence. In situations where the results are significantly different at 95%, then it can be said that we are 95% confident that the numbers are different. Note that there is 5% chance that the numbers are not significant due to sampling error (Rutherford, 2012).
Managerially important differences: when the results are different to a level that the difference raises concerns from a managerial position, then it can be argued that the difference is managerially important. For instance, the difference in the satisfaction score for two health and insurance plans may be statistically significant, yet so tiny to be of managerial significance or to be of little practical significance.
Results can be statistically significant and still do not have managerial importance. The fact that results show that they are statistically significant does not mean that they must have managerial importance. Statistical significance can be interpreted differently, depending on the particular situation. It is also possible that numbers or results to be different in the mathematical sense, but still not statistically different in a statistical sense (Muller and Fetterman, 2002).
Here are the steps for testing any hypothesis:
Step 1: First, state the H0/ Null hypothesis and the Ha/ alternative hypothesis (Rutherford, 2001). The alternative hypothesis stands for the statement that the researcher is trying to prove (Rutherford, 2001). The null hypothesis, on the other hand, represents the negation of the statement that the research is attempting to show (Rutherford, 2001).
Step 2: State the sample(s) size(s).
Step 3: Reveal the test statistic that will be adopted in carrying out the hypothesis test
Step 4: Identify the critical test value. The value stands for the cutoff point for the experiment statistic (Rutherford, 2001). In case the null hypothesis (H0) was true, then there would only be a probability of attaining a test statistic value that would be at least to this extent/ extreme (Rutherford, 2001). In case the test statistic value estimated from the sample data is more than the critical value, then the decision will be arrived to by rejecting the null hypothesis and accept the alternative hypothesis (Rutherford, 2001).
Step 5: Compute the test statistic value, using the sample data (Miller, 1997).
Step 6: Decide based on the comparison of the critical value of the test and the computed test statistic, whether to accept null hypothesis or to reject it for the alternative hypothesis (Miller, 1997). Where the p-value has been calculated, then the decision is made based on a comparison of p-value against. In case, the p-value is greater than , then reject H0 (Miller, 1997).
ANOVA
Dependent variable: sales per year
Independent variable: Promotion expenditures per year
DF = 1 Numerator, this is df1 –degrees of freedom
DF = 19 Denominator, this is df2 –degrees of freedom
Therefore,
df1 = 1
df2 = 19
Where,
df1 = k-1 and
df2=N-k
Test with:
a =0.05,
df1=1, and
df2=19
F = MSA / MSE
F = 34,276/ 4,721
F = 7.2603
Critical value from the table 8.2
Decision Rule
We reject the null hypothesis H0 when the F (Observed) is higher than F (critical value) (Muller and Fetterman, 2002). In our case, 7.2603>8.2, therefore we accept the H0. Therefore, we can conclude that there is a relationship between the number of sales and the sales promotion expenditures. When sales go higher, there is need to spend more on promotions (Muller and Fetterman, 2002).
References
Miller R. (1997). Beyond ANOVA: Basics of Applied Statistics. CRC Press Publishers.
Rutherford A. (2012). ANOVA and ANCOVA: A GLM Approach. Second Edition. John
Wiley & Sons Publishers
Rutherford A. (2001). Introducing ANOVA and ANCOVA: A GLM Approach. SAGE
Publishers.
Muller K.E., and Fetterman B.A. (2002). Regression and ANOVA: An Integrated Approach
Using SAS Software. SAS Institute Publishers
