For the month of June this blog had:

• 329,576 hits
• 98,242 page-views
• 18,556 visits
• 13,707 unique visitors

The above list does not include 51,120 hits and 50,231 page-views from robots, crawlers, worms and other similar traffic sources. In other words, the above list is human only; that’s a lot of eyeballs! Here is the same information in a bar graph:

My highest trafficked day was June 18th with 43,827 page-views spread over 7,570 visits. Yup, that was the day I was listed on fark.com for this post about the similarity between John McCain and Colonel Tigh from Battlestar Galactica.

This blog is also syndicated via RSS to an average of twenty readers, with a high of 76 readers on June 18th. My facebook profile also pulls a short excerpt of each post and broadcasts it via RSS to my 397 friends.

The five most viewed posts on this blog for the month of June were:

1. Battlestar Politica – 9308 page-views
2. Casting Call for New Bruce Willis Film, The Surrogates – 739 page-views
3. Centralization vs. Decentralization – 655 page-views
4. Kevin Garnett a Celtic: We’re Baaaack! – 563 page-views
5. U.S. GAAP vs. International GAAP vs. Unified GAAP – 440 page-views

Finally, the five most used search keyphrases that brought visitors here were:

1. pieniazek
2. anova test
3. photo
4. ronald jenkees
5. finite population correction factor

If there are any other statistics anyone would like to see let me know and I’ll add them (if possible). Thanks to everyone for making June my best month yet! You all rock!

1. small dog create

Huh? Was this person asking Google to make them a small dog?

2. too much fun but not enough education

There is a fine balance. One which many strive for but few attain.

3. sitting

Where they looking for a how to? Definition? History?

4. managerial accounting for idiots

How much you wanna bet a Fortune 500 CEO is behind this search?

5. i love nate and adam icons for aim

No idea why I’m the first result for this…

6. do schools need textbooks

College kid trying to convince his/her professor to drop textbooks? Or a principal trying to cut costs? In my opinion, schools do not need textbooks but do need authoritative resources to learn from, whether they be people or e-books or experiences is up to the school or teacher.

OK, time to go Google “Large pile of cash create”.

Through the months, all of this blog’s crucial statistics have improved (on pace to blow out my high mark for unique visitors tonight), except one: comments!

So, in an attempt to increase those numbers, this contest will be very simple; simply comment on this post and you’ll entered for a chance at Ronald’s awesome CD! For those who don’t want to wait a week, you can order Ronald’s debut album directly from his blog.

At the end of the contest, all comments will be reviewed and all valid comments (not spam) will be tossed into a pool and randomly chosen. You can comment on anything you want, but I’m interested in how you first heard about Ronald Jenkees and what do you think of his music?

This contest will end next Monday at midnight. Make sure you leave an e-mail address when commenting so I can get in contact with the winner. Good luck!

A 4.0 GPA for the Spring ’07 semester! I got an A in both courses, Fundamentals of Marketing and Quantitative Tools for Management (aka Statistics II) during this semester. Pretty awesome, eh?

This is in addition to the A I earned for the Principles of Management class during the Winter ’07 semester:

So that’s three classes down, twelve more to go. Hopefully I can keep this up…

An ANOVA test, is in essence a method to determine of three or more population means are equal. It is useful because there are many scenarios for which we do not want to know the exact difference between population means, only if they are equivalent. It is also a relatively simple method to calculate if the population means are roughly equal or vastly different. The ANOVA test requires that the populations being tested are normally distributed, have equal variances and that the samples are independent of each other.

The ANOVA test uses the variation between samples within a category and between categories. For instance if we’re testing whether golf ball A, B and C travel the same distance, the ANOVA test utilizes the differences between the means of A, B, and C and also the differences in means of the samples within A, B, and C. The ANOVA test basically compares these two variations (between categories and within categories) and if the variation between categories is relatively high compared to the within categories variation, then the ANOVA test will lead us to reject the null hypothesis (that all population means are equal). This works because if the variation within categories is fairly clustered and the variation between categories is fairly spread out, then the categories cannot, logically, be equivalent, as the within variation shows that each sample is following some pattern.

Furthermore, the ANOVA test is more reliable than using three separate (for instance hypothesis) tests, as three unique tests will compound the confidence level, thus decreasing our confidence in the test.

Looking at figure 6-8*,

we see that the x values with the highest frequency are 10 and 18, the lower and upper limits of the x values, respectively. This population is not exactly symmetrical but is close to being so, as it closely resembles a “U” shape. Figure 6-9* shows the distribution of the average mean of 3 x values chosen at random, 3000 times.

Even though 10 and 18 are the most common x values in the population, there are only a few average mean x values in the distribution in figure 6-9. In order to have a sample mean of 10 or 18 all three x values in a random sample would be to be all 10 or all 18. Thus the probability of choosing three 10′s or three 18′s in a random sample is quite low, thus why the distribution for 10 and 18 is so low in figure 6-9. Moving to the middle of figure 6-9, shows a rise in the number of occurrences of the sample means ranging from 13 to 16. Again, this makes sense because there are many more ways a sample mean could be in the 13 to 16 range and thus would be more commonly chosen in a random sample. Since an increasing amount of sample means will lie in the middle of the range, the standard deviation will be lower than the total population, as a higher proportion of the values will be closer to each other; whereas a high proportion of the values for the population in figure 6-8 lie at the upper and lower limits of the range, thus increasing the probability that the deviation between any two randomly chosen values will be higher.

Looking at figure 6-8, an eyeball estimate would lead me to say the median for this population would lie somewhere between 13 and 15. Figure 6-9 is showing that for 3,000 random samples of size 3, it is more likely the average mean will be close to the median than at the upper or lower limits [in this example, the median is equal to the mean of the total population, this is not always the case and when the median and mean are not equal the middle (and highest point for a high sample size) of the distribution in figures 6-9 and 6-10 will approach the mean].

By increasing the sample size to 10, and thus increasing the reliability and accuracy of the results, figure 6-10* is showing that as more and more x values are included in the sample, the sample mean will approach the population mean because the chance of picking ten x values that average out to be similar to the population mean is higher than in a sample of three. Since the likelihood of ten random values equaling the population mean is higher in figure 6-10, the population mean is the value most often represented in the 3,000 random average means. Likewise, since the likelihood of the average mean of ten random values being equal to or close to the upper or lower limits is low, these values are either not represented or much less so than the population mean. The principle behind figure 6-10 is that if 3,000 random samples were taken, with a sample size close to or equal to the population size, the average means would all come out close to or equal to the population mean, the proximity of the sample size to the population size determines the range of the distributions we see in figures 6-9 and 6-10 and increases (if sample size is not close to population size) or decreases (if population size and sample size are close or equal) the deviation between values. If the sample size was close to or equal to the population size, the standard deviation would be close to or equal to zero (as most of the average means would be equal to the population mean).

The idea being shown through these three figures is the Central Limit Theorem, which in essence states that as a sample size increases, so does the resemblance of the sample distribution of the average means to a normal distribution (e.g. the shape shown in figure 6-10).

*All graphs are courtesy of Course in Business Statistics 4th Edition by David F. Groebner, Patrick W. Shannon, Phillip C. Fry, and Kent D. Smith

In general, as the sample size decreases in a t distribution, it becomes more and more similar to a z distribution. As the sample size increases, the standard deviation decreases in both z and t distributions. In essence, a larger sample size leads to a more accurate end result. The exponential decline in differences between the t and z distribution is an outcome of the central limit theorem. As the standard deviation decreases (due to the increased reliability of an increasingly larger sample size), the differences between the two distributions are so accurate that they both approximate a standard normal distribution.

In the real world, we see this principle in practice all the time, as I’ve mostly been a windows user, more time with Mac OS X will decrease the amount of times I use control-c for copy instead of apple-c; [although WebCT threw me for a loop since it still uses control-c as does OpenOffice.org]. It’s the basic concept behind learning, the more information you take in the smarter you’ll be until you’re very nearly perfect (time plays a factor as you can’t learn everything in a life time) and a very pervasive concept in business; the more cars Honda makes in the exact same manner, the fewer mistakes there’ll be. If their new plant made a car that wouldn’t start in their first batch of five cars, the 20% failure rate is not very indicative of Honda quality. You would expect that as they made a million of the same model they’re failure rate would be much, much lower. Each million cars produced should bring their failure rate closer to 0%. If it doesn’t then their is a flaw in the manufacturing process.

When a sample is greater than 5% of the population from which it is being selected and the sample is chosen without replacement, the finite population correction factor should be used. The adjusted z-value would be larger than the normal z-value, meaning that the value is more standard deviations from the middle than in a non-adjusted z-value.

This factor adjusts the z-value to show the extra precision obtained from the sample size being a greater fraction of the population size than normal. Since the standard deviation becomes smaller as the sample size increases, the FPCF shows that a value in a large sample size not at or near the mean is a greater number of standards deviations from the mean than in a small sample size. In other words it’s rarer for a value in a large sample size to be far away from the mean compared to a small sample size.

University of Massachusetts at Amherst Network Stats:

No suprises here, Sublime and Family Guy top their respective charts, half the school is apparently not interested (or at least not affiliated) in politics, maybe that has something to do with the fact that a 1/3 of the campus is single and on the prowl?

Northeastern University Network Stats:

Northeastern has some similarities with Umass, a lot actually. 1/3 of the campus is single and 1/2 are not affiliated with a political view, the top TV show is Family Guy and the top book, like Umass is Harry Potter.

University of North Carolina at Chapel Hill Network Stats:

Hey, here’s something interesting, UNC has only 1% less students who call themselves “liberal” (18%) than Northeastern and Umass (both at 19%)! Harry Potter once again tops the books list, but the Bible (something not on either of the other two networks) comes in at #2! facebook also backs up the popular claim that there are more girls than boys at the campus (46% female to 35% male).

In general, all three campuses have pretty much the same interests even though they have slightly different demographics. There’s some grumblings on the Northeastern network page about the “masculinity” of their campus due to Jack Johnson being the #1 musical artist but at least they don’t have Coldplay topping their charts like UNC! Sorry Coldplay fans, no me gusta…and of course Ben Folds joins the top ten list (they are from Chapel Hill), and the Fray make it into UNC’s top ten list.

University of Southern California Network Stats:

From my personal experience at USC, the campus was a great source of new music and movies as many of the students had connections within the music industry either through friends in bands, or internship experience and of course the USC Film School is one of the best such programs in the country so I was expecting for USC’s musical and cinematic preferences to be different from other schools, yet the facebook network stats doesn’t back up this hypothesis. There are some slight differences, for instance USC has Gladiator and Zoolander in it’s top ten movies and John Mayer in it’s top ten music list, but other than those two slight differences, USC students like the same things UNC, Umass, and Northeastern students like. Not a very groundbreaking statement there, considering how students from everywhere attend schools everywhere and we’re all so connected it’s tough not to watch the same movies and listen to the same songs.

Let’s see if these stats change any for the City of Boston network:

Aaargh, Coldplay at #1 again. Other than Rap and R&ampB making their way into the top ten list, there’s not much of a difference between the Boston network page and the four colleges we’ve looked at. Looking at a few of the other cities across the country generally leads to the same results. There are differences in musical tastes between say Cincinatti, Ohio and Boston, Massachusetts but not a huge difference. What does this conformity say about our society? Are we all really that similar?