## Thursday 26 April 2012 In this study, the researcher wanted to determine whether a resemblance or difference exists in the behavior of direct and rented referrals based on their clicks per day and consistency in clicking. Thus, the study has the following stated problems:
1) Is there a significant difference in the clicks per day between direct and rented referrals?
2) Is there a significant difference in the variances of clicks per day between direct and rented referrals?

Via the utilization of Yamane’s formula for the computation of the sample, 246 direct referrals (from a population of 639) and 278 rented referrals (from a population of 912) were randomly chosen in order to attain a 95% level of confidence. The use of a random sample is deemed important in order to make inferences free from any form of bias. Furthermore, the assumptions of normality and homogeneity were also met in order to arrive with credible results. The study was conducted for 3 months, upon which thorough observations were made. It was made sure that the randomly selected direct and rented referrals were marked so that the researcher may be guided that they were part of the sample. In addition, rented referrals were made sure that they have not been auto replaced during the conduct of the research. Independent t-test was used in order to answer the first stated problem while a Levene’s test was used for the second. The following are the statistical results for the study:

 Group Statistics Kind of Referral N Mean Std. Deviation Std. Error Mean Average Clicks Rented Referrals 278 .61888 .218750 .077340 Direct Referrals 246 .71588 .791992 .280012

The table above showcases the descriptive statistics for the study. The column of interest here would be that of the “Mean” and “Std. Deviation”. Let us first take a look at the “Mean” column. Well in case you don’t know, “Mean” simply refers to the average. The numerical values being shown in this column simply points out the average clicks of rented and direct referrals for each day. Here we can see that direct referrals would usually have a higher average in clicks (mean of 0.72) than rented ones (mean of 0.62) for each day. Although we can see that there’s a difference, in statistics, we do not simply base our conclusions by looking at these values. Later, we will make use of a statistical tool that will inform us whether the difference is significant or not. Moving on to the next column labeled “Std. Deviation”, here we can again see that direct referrals have a higher std. deviation (0.792) as compared to rented referrals (0.219). Standard deviations pertain to dispersion. Simply said, it refers to how far each referral’s click per day is away from the computed mean. A low std. deviation would signify that most of the referral’s average click for each day is near the computed mean while a high std. deviation would tell us that most of the referral’s average click for each day is far from the computed mean. Relate this to rented and direct referrals, this would mean to say that rented referrals (having a low std. deviation) would usually have averages that are near each other (just a thought: in some PTC sites notice how rented referrals would behave? Now they click, now they don’t. There is no rented referral that would click always and all of them behave in the same manner, thus the result in std. deviation).   Meanwhile, direct referrals having high std. deviation would usually have averages situated away from the mean. Take time to observe the averages of your direct referrals, notice that their averages are of the extremes, some very low and some very high because direct referrals who are not convinced of the PTC site would simply quit (thus, the very low average) while those who see it as an opportunity for income keep on clicking (thus, the very high average). Again, although we can see a difference in the std. deviations of rented and direct referrals, as of now, conclusions are improbable without the use of the appropriate statistical tool.

In order for us to finally address our stated problems, we make use of the table as shown below:
 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference Lower Upper Average Clicks Equal variances assumed 9.080 .009 -.334 14 .743 -.097000 .290496 -.720052 .526052 Equal variances not assumed -.334 8.062 .747 -.097000 .290496 -.765991 .571991

In relation to problem one, the column with most relevance would be that of Sig. (2-tailed) located under “t-test for equality of Means”. Observe that there are two values found in that column. Since the variances are heterogenous (let me not explain this further to avoid complexities, but if you really want to then send an e-mail), we would be using the value below (the one in line with the row “equal variances not assumed”). Notice that the value we are referring to is 0.747. This value will be used in order for us to give a statistically reasonable answer to our first stated problem. A Sig. (2-tailed) value of more than 0.05 (in which case our value, 0.747 is) indicates that there is no significant difference between the clicks per day of rented and direct referrals. This means to say that although there is a difference in the clicks per day of rented (0.62) and direct (0.72) referrals, the difference is not big enough that we can say it is statistically significant. Simply said, the difference that we can see in the clicks per day of rented and direct referrals may simply be due to chance alone. This also means that, in the study conducted, direct referrals do not necessarily have more clicks as compared to the rented referrals because the difference is quite small.

In relation to problem two, the column with most relevance would be that of Sig. located under “Levene’s Test for Equality of Variances”. The Sig. value that we have over here will inform us whether the variances in the clicks per day of rented and direct referrals have a significant difference or not. Since the Sig. value (0.009) is less than 0.05, we can say that indeed the variances of rented and direct referrals have a significant difference. Remember, the std. deviations we discussed earlier? Well a standard deviation is the square root of a variance so their relevance is almost the same. Having this in mind we can then infer that the std. deviation of rented referrals (0.218) and direct referrals (0.792) have a significant difference. This proves the discussion that we’ve had earlier that rented referrals have averages situated near the mean because they somewhat behave in the same way (now they click, now they don’t) while direct referrals have averages that are mostly away from the mean because they behave differently (probably, some quit so they have low averages while others are really into it so they have high averages).

All in all the results of this study point out that although direct referrals clicks a little bit more compared to rented ones, the difference is not big enough for us to conclude that it is statistically significant. Apart from that, this study also points out that there is a significant difference in the variances of clicks per day between rented and direct referrals.