One Fish, Two Fish, Oh God, More Fish
It’s Storm ‘n Hail time up here in Calgary! Don’t believe me? Check out these pictures/videos taken last Tuesday when a huge storm barreled through the southern part of the city.
I love that picture of the lightning behind the Calgary Tower.
I also love that #ABstorm is a hashtag, and one that gets used quite frequently at that.
DONE!
Olympics?
Dude, how cool would that be if the Olympics came back to Calgary? And 2026 is a good year: it’ll be my 20th blogging anniversary year!
Seriously, though. The city already has most of the equipment and facilities for the winter Olympics; they’d likely need some updating/renovation, of course, but still. It’d be pretty cool if the city agreed to bid and we actually won.
CALGARY WINTER OLYMPICS 2026!
Week 27: The Kruskal-Wallis One-Way Analysis of Variance by Ranks
Back to nonparametrics this week with the Kruskal-Wallis one-way analysis of variance by ranks!
When Would You Use It?
The Kruskal-Wallis one-way analysis of variance by ranks is a nonparametric test used to determine if, in a set of k (k ≥ 2) independent samples, at least two of the samples represent populations with different median values.
What Type of Data?
The Kruskal-Wallis one-way analysis of variance by ranks requires ordinal data.
Test Assumptions
- Each sample of subjects has been randomly chosen from the population it represents.
- The k samples are independent of one another.
- The dependent variable (the values being ranked) is a continuous random variable.
- The distributions of the underlying populations are identical in shape (but do not have to be normal).
Test Process
Step 1: Formulate the null and alternative hypotheses. The null hypothesis claims that the k population medians are equal. The alternative hypothesis claims that at least two of the k population medians are different.
Step 2: Compute the test statistic, a chi-square value (usually denoted as H). H is computed as follows:
Step 3: Obtain the p-value associated with the calculated chi-square H statistic. The p-value indicates the probability of observing an H value equal to or larger than the observed H value from the sample under the assumption that the null hypothesis is true. The degrees of freedom for this test are k – 1.
Step 4: Determine the conclusion. If the p-value is larger than the prespecified α-level, fail to reject the null hypothesis (that is, retain the claim that the population medians are equal). If the p-value is smaller than the prespecified α-level, reject the null hypothesis in favor of the alternative.
Example
The example for this test comes from my music! Looking at my songs that are rated five stars, I wanted to see if there was a difference in the median playcounts for the different genres. Since my Five Star songs are mostly electronic and alternative, I decided to group the rest of the genres into an “other” category so that there are three genre categories total. Here, n = 50 and let α = 0.05.
H0: θelectronic = θalternative = θother
Ha: at least one pair of medians are different
To obtain the ranks of the songs, I did the following steps:
First, I sorted the songs by playcount.
Second, I ranked the songs from 1 to 50 based on their playcount, with 1 corresponding to the song with the highest playcount and 50 corresponding to the song with the lowest playcount. Note that I could have done this the opposite way (1 corresponding to the least-played song and 50 corresponding to the most-played song; the resulting H value would be the same).
Third, I adjusted the ranks for ties. Where there were ties in the playcount, I summed the ranks that were taken by the ties and then divided that value by the number of tied values. I then replaced the original ranks with the newly calculated value.
Finally, I summed the ranks within each of the three genre groups to obtain my Rj values. Here is a table of this final procedure:
Computations:
Here, our computed p-value is greater than our α-level, which leads us to fail to reject the null hypothesis, which is the claim that the median playcount is equal across the three genre groups.
Example in R
No example in R this week, as this is probably easier to do by hand than using R!
Ego boost
‘Sup.
So I picked up all my TA evaluations a few days ago because the department gets rid of them once you’ve graduated and I wanted to make sure I picked them up before I forgot to do so.
Anyway, today I feel like useless garbage (I mean, even more so than normal), so I decided to get a little ego boost from the reviews. These are my favorite comments.
- “Best TA I’ve had”
- “I feel like she can teach better than prof”
- “I have nothing but amazing things to say about her”
- “She could easily be a professor”
- “It is evident that she cares about students’ success”
- “Claudia has helped and taught me more than any of my other teachers”
- “Very friendly and welcoming and is good at creating a fun environment for learning”
- “Goes through questions and tells you information that not even the prof mentions”
- “She is very, very good (better than my prof)”
- “Should be offered a job should the need arise”
- “One of the best TAs I’ve had over my 4 years”
- “I found her lab sessions and office hours were highly beneficial to my learning (even better than the lectures)”
- “She is a very good teacher, gifted at it even”
- “Learned better from her labs than lectures”
- “She is the bomb”
LEIBNIZ DAY 2016
IT’S LEIBNIZ DAY, MOTHERFUCKERS!
Love, love, love.
It’s too bad I feel like an absolute worthless bag of trash today. Leibniz day is a day to be happy.
BOOSH boosh BOOSH boosh BOOSH I’m gonna go cry for a little while.
June walking!
So June was a good walking month. In all, I walked 392.78 miles in 850,144 steps. I spent 94 hours and 47 minutes walking (almost four days), which is super awesome.
Oh, and today I walked a marathon. Or a little bit further: 26.51 miles. That’s a new daily record for me by about 4 miles. WOO!
Graph of distances per day!
Only three days with distances less than 10 miles and only seven days with distances less than 15 miles? I’ll take it.
Also, if this were to ever be my monthly pace, I could hit 4,700 miles in a year.
ONWARD TO JULY!
*breaks down your front door* HAVE YOU HEARD THE LATEST NEWS ABOUT THE KILOGRAM??
I’ve done a couple of posts about the kilogram, and if you’ve read any of them (or have done any reading about the SI units at all (‘cause that’s a common interest, right? (I mean, I can’t be the only one (…right?)))), you know that the kilogram is the only one of the basic seven measures that is still defined by a physical object rather than a calculation or constant.
Specifically, the mass of the kilogram is defined by an egg-sized alloy of platinum and iridium. This little dude sits beneath not one but three glass bell jars ion a climate-controlled, hermetically sealed room in Paris. Why? Because it’s the object that defines the kilogram, meaning that it is the benchmark against which all other kilograms are compared. So if it changes weight—due to dust or residue or moisture—the kilogram itself changes weight. In fact, it’s so important that the kilogram remains unchanged that it is only removed from its prison every 40 years in order to compare it to other similar replicas that are stored around the world.
These issues with the physical copy are the main reasons why scientists wish to define the kilogram with something that is an inherent standard in nature—like the speed of light or the wavelength of photons. For quite some time, physicists have been considering using the Planck constant as part of the definition of the kilogram. Specifically, the Planck constant could be used in conjunction with Einstein’s E = mc2 equation in a way that could determine mass solely through physical constants. However, no one has yet been able to actually measure the Planck constant to a level of precision that would surpass that of using the physical kilogram as the standard.
However, based on the current pace of progress, physicists suspect that they might be able to redefine the kilogram in terms of the Planck constant by as early as 2018, rendering Le Grand K, as the physical kilogram is known, obsolete.
Crazy, huh? Check out the article here!
Walk-a-ma-thon
I’ve had a good week as far as walking goes. From Monday the 20th until today, I’ve walked a total of 136.1 miles in 296,578 steps. Graph!
(Ignore Friday.)
ALSO! Yesterday was the first time I was able to hold an average pace of 4.5 MPH for 20 miles. I guess I’d never really tried for that before, but my average pace is usually around 4 to 4.2 MPH. So it’s an improvement, at least.
WOO!
Week 26: The Single-Factor Between-Subjects Analysis of Variance
We’re back to parametric tests this week with the single-factor between-subjects analysis of variance (ANOVA)!
When Would You Use It?
The single-factor between-subjects ANOVA is a parametric tests used to determine if, in a set of k (k ≥ 2) independent samples, at least two of the samples represent populations with different mean values.
What Type of Data?
The single-factor between-subjects ANOVA requires interval or ratio data.
Test Assumptions
- Each sample of subjects has been randomly chosen from the population it represents.
- For each sample, the distribution of the data in the underlying population is normal.
- The variances of the k underlying populations are equal (homogeneity of variances).
Test Process
Step 1: Formulate the null and alternative hypotheses. The null hypothesis claims that the k population means are equal. The alternative hypothesis claims that at least two of the k population means are different.
Step 2: Compute the test statistic, an F-value. To do so, calculate the following sums of squares values for between-groups (SSB) and within-groups (SSW):
Then compute the mean squared difference scores for between-groups (MSG) and within-groups (MSE):
Finally, compute the F statistic by calculating the ratio:
Step 3: Obtain the p-value associated with the calculated F statistic. The p-value indicates the probability of a ratio of MSB to MSW equal to or larger than the observed ratio in the F statistic, under the assumption that the null hypothesis is true. Unless you have software, it probably isn’t possible to calculate the exact p-value of your F statistic. Instead, you can use an F table (such as this one) to obtain the critical F value for a prespecified α-level. To use this table, first determine the α-level. Find the degrees of freedom for the numerator (or MSB; the df are explained below) and locate the corresponding column on the table. Then find the degrees of freedom for the denominator (or MSE; the df are explained below) and locate the corresponding set of rows on the table. Find the row specific to your α-level. The value at the intersection of the row and column is your critical F value.
Step 4: Determine the conclusion. If the p-value is larger than the prespecified α-level (or the calculated F statistic is larger than the critical F value), fail to reject the null hypothesis (that is, retain the claim that the population means are all equal). If the p-value is smaller than the prespecified α-level, reject the null hypothesis in favor of the alternative.
Example
The example I want to look at today comes from a previous semester’s STAT 217 grades. This particular section of 217 had four labs associated with it. I wanted to determine if the average final grade was different for any one lab compared to the others. Here, n = 109 and let α = 0.05.
H0: µlab1 = µlab2 = µlab3 = µlab4
Ha: at least one pair of means are different
Computations:
For this case, the critical F value, as obtained by the table, is 2.70. Since the computed F value is smaller than the critical F value, we fail to reject H0 and conclude that the average final grade is equal across all four labs.
Example in R
x=read.table('clipboard', header=T)
attach(x)
summary(fit)
Df Sum Sq Mean Sq F value Pr(>F)
lab 3 1319 439.5 2.036 0.113
Residuals 105 22670 215.9
R will give you the exact p-value of your F statistic; in this case, p-value = 0.113.
Internet Garbage
Because I’m garbage, too! And I already did a June List, so I can’t use that as an excuse to post this worthless nonsense.
Anyway.
Have some awesome pasta. How good does this look? So much cheese.
Or some writing material.
Miss Trunchbull’s cake, maybe?
Pancakes. Pancakes are always good.
That’s all I got. Sorry, in thesis stress mode. It’s not a happy place.
Say Yes to the Stress
If you’re stressed about the future, clap your hands
*clap clap*
If you’re stressed about the future, clap your hands
*clap clap*
If you’re stressed about the future
And you don’t care about rhymes because you’ve got bigger things to worry about and you should be doing something more productive than blogging about stupid nonsense and trying to make light of your own panic but you can’t because you’re stressed and panicking and freaking out
If you’re stressed about the future, clap your hands!
(*clap clap*)
Calgary’s river walk public bathrooms are like little rave party boxes
Dudes. Okay. So Calgary has this awesome bike/walking path alongside the Bow River downtown. It’s like the Moscow-Pullman trail, only nicer ‘cause it’s alongside a river and not that damn highway. It’s also got shade.
Anyway, I was doing a 20-mile walk this afternoon and spent most of that walk on the river path. While I was down around Centre Street, I noticed some dude going off the path to get water at a drinking fountain (which I had probably seen before, but never really paid attention). But then, I noticed for the first time that the little building thingies by said drinking fountain were actually bathrooms.
And awesome bathrooms, at that. They’re like these little boxes from the future. You press a button to open the door; once you’re inside, it seals you in and turns everything blue and a voice tells you that you have a maximum of 10 minutes to do your thing. The toilet seat is controlled by a button, the toilet paper is controlled by a button, and the toilet automatically flushes once you wash your hands. Check out the inside of this thing:
RAAAAAAAAAAAAVE!
Yes, those are black lights. And there was thumping bass rave music playing.
I don’t know if these were commissioned by Mayor Nenshi, but if they were, that man has definitely earned his World Mayor title.
Edit: lawl, they’re a Pokestop.
Pretty City
I love Calgary, man. I just really, really like it as a city. It’s big (population- and area-wise), and I always like the business of a big city (especially downtown) but there are also a lot of places you can go where it feels like you’re living in a small little town.
It’s also great to walk around the city (in the places where there are sidewalks). I’ve been utilizing the paths down by the river a lot recently, and I really just like the feel of everything going on down in that area. It feels like home.
Here’s a video of time lapse footage of parts of the city. Tell me Calgary isn’t beautiful.
I’m so excited to have found the love of my life here. I look forward to spending a long, long time in this city.
(It’s hard for me to say “the rest of my life” with respect to staying in one place, just because I’ve moved around so freaking much. But that’s ultimately what I’d like, I think.)
Week 25: The McNemar Test
Ready for more nonparametric tests? Today we’re talking about the McNemar test!
When Would You Use It?
The McNemar test is a nonparametric test used to determine if two dependent samples represent two different populations.
What Type of Data?
The McNemar test requires two categorical or nominal data.
Test Assumptions
- The sample of subjects has been randomly chosen from the population it represents.
- Each observation in the contingency table is independent of other observations.
- The scores of the subjects are measured as a dichotomous categorical measure with two mutually exclusive categories.
- The sample size is not “extremely small” (though there is debate over what constitutes an extremely small sample size).
Test Process
Step 1: Formulate the null and alternative hypotheses. For the McNemar test, the data are usually displayed in a contingency table with the following setup:
Here, Response 1 and Response 2 are the two possible outcomes of the first condition. Response A and Response B are the two possible outcomes of the second condition. Cell a represents the number of people in the sample who had both Response 1 and Response A, cell b represents the number of people in the sample who had both Response 1 and Response B, etc.
The null hypothesis of the test claims that in the underlying population represented by the sample, the proportion of observations in cell b is the same as the proportion of observations in cell c. The alternative hypothesis claims otherwise (one population proportion is greater than the other, less than the other, or that the proportions are simply not equal).
Step 2: Compute the test statistic, a chi-square. It is computed as follows:
Step 3: Obtain the p-value associated with the calculated chi-square. The p-value indicates the probability of a difference in the two cell counts equal to or more extreme than the observed difference between the cell counts, under the assumption that the null hypothesis is true.
Step 4: Determine the conclusion. If the p-value is larger than the prespecified α-level, fail to reject the null hypothesis (that is, retain the claim that the cell proportions for cell b and cell c are equal). If the p-value is smaller than the prespecified α-level, reject the null hypothesis in favor of the alternative.
Example
The example for this test comes from a previous semester’s STAT 217 grades. In the semester in question, the professor offered the students a “bonus test” after their midterms. This was done by allowing the students to essentially re-take the midterm given in class, but doing so on their own time and using all the resources they wanted to. A (small) fraction of the points they would earn on this bonus test would be added to their actual in-class test points.
I wanted to determine if the proportion of students who passed the lab test and failed the bonus test was equal to the proportion of students who failed the lab test but passed the bonus test, using n = 109 students and α = 0.05.
H0: πpass/fail = πfail/pass
Ha: πpass/fail ≠ πfail/pass
The following table shows the breakdown for the four possible outcomes in this case.
Computations:
Since our p-value is smaller than our alpha-level, we reject H0 and claim that the proportions for cells b and c are significantly different.
Example in R
Since the calculations for this week’s test are quite easy, it’s probably faster to do them by hand than use R!
Three words:
I
am
garbage.
WGOSDFKL
We have to travel tomorrow and I’m feeling anxious about it. Have a survey.
Can you stay inside all day without getting bored?
Yeah, but only every once and awhile. I need to go do my walking or I get really anxious.
Tell us a TV show that we should watch.
Community is the best freaking thing, yo.
When was the last time you were at your home computer all day?
ALL day? I’m not even sure.
What websites other than your own do you visit daily?
Ye olde standards. Reddit, Facebook, Tumblr, YouTube, emails.
Do you have a favorite day of the week? Why?
I’ve always liked Tuesdays for whatever the hell reason. Fridays are Fridays, of course, but Tuesdays have always just been nice days for me, regardless of what’s going on in my life.
Did you ever watch Saturday morning cartoons? What was your favorite?
I usually had Cartoon Network on at my dad’s on Saturdays, yes, but I much preferred the Friday night stuff. I remember when Adult Swim started, haha.
Were you a comic book fan?
Nopers.
Did you earn an allowance when you were a kid? How much? Was it tied to chores?
Maybe for a little bit with my mom; I can’t really remember. My dad would give me $20 to spend at the mall on weekends, but I think he just did that to give me something to do while he went to Hallmark.
What is the fanciest type of car you’ve ridden in? What occasion?
I’m trying to remember if I’ve actually been in a limo, or if I’m just making nonsense up. I honestly am not sure.
What’s your favorite sport to watch?
Baseball!
Ever tried surfing?
Nope. And I don’t really have any desire to.
Have you ever been to a live major team sporting game?
Nate and I went to the Giants/Braves game in San Francisco.
From a scale of 1 to 5 how athletic are you (1=nerd, 5=very athletic)?
Um…3? I have no idea.
What’s your favorite horror movie?
Not a horror movie fan. Unless Final Destination counts in this category. If so, Final Destination, the original, or Final Destination 2.
What is your favorite cult classic movie?
Tremors! That counts.
About how many times do you go to the movies a month?
It probably averages out to about 0.16 times or so.
Favorite movie, which one came to your head first?
Sunshine. It will always be Sunshine.
What if your life was like a movie? What type of movie would it be?
Not a movie I’d ever want to watch, lemme tell ya.
Do you like long series movies, like “Lord of the Rings”?
Not in particular. I’m not a big movie person in general.
(My titles suck, sorry)
Hahaha. This is great.
(Sorry for the garbage blogging; I’ve just kind of been in panic mode about everything lately.)
BLAH BLAHSON
UGH.
So today was supposed to be a good day. I was supposed to go to the Faculty of Science awards ceremony and get my TA award thingy and everything was supposed to be great.
But instead I had a panic attack.
I’m calmer now (obviously; can’t write a blog in the middle of a panic attack), but I’m sitting in my office with a really bad headache and a really high degree of self-hatred. I mean, I’m never too thrilled with myself, but it’s been awhile since I’ve just felt so damn worthless.
UGH.
Quaz
Want to know what character trope you are? Quizzy here.
I’m the Villain, apparently, which kind of surprises me. But hey, I’ll take it.
I Have Money and I want Headphones
AS THE TITLE SAYS, I have money and I want headphones.
The money’s from MTurk. I’ve been doing three or four little tasks at night, and while the individual tasks don’t pay much (maximum like $2 for any of the ones I do), if you do enough, they add up. I have about $50 from MTurk now, so I’ve decided I can spend that on whatever I want.
But it’s not like I need headphones. I have my awesome Koss ones that cost about $4.50 and I have at least 4 backup pairs of them for when the current ones inevitably break (the sound quality is awesome, but they don’t last too long. $4.50 headphones, yo).
But I logged onto Amazon for whatever the hell reason tonight and it knew I had some extra money ‘cause it was like, “hey bro, y u no buy some Sennheisers?”
And so it’s all Amazon’s fault that I’ve spent the past two hours looking at headphones.
Front runners:
- Sennheiser HD 518 Headphones
- Sennheiser HD 280 Pro Headphones
- Sennheiser HD 598 Special Edition Over-Ear Headphones
I cannot choose!
Edit: Okay, I ended up not getting any of these. I ended up not getting Sennheisers at all. Instead, I got this guy. I’m super picky about comfort when it comes to headphones, and a good number of the reviews for these headphones said that they were really, really comfortable. Plus they’re supposed to sound good. And they’re a cool shade of blue.
I SUCK AT LIFE
I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck I suck
I SUCK
Claudia vs. Emojis
Okay, I know I did a blog post on emojis not too long ago, but holy hell. Now I have a smart phone and I can see the insanity firsthand.
I mean, I get it. Some of these are actually useful and/or sensible. Like the regular smileys. I use regular smileys over Skype and Facebook and whatnot to indicate sarcasm, mood, good-natured jesting, whatever.
But then it gets weird.
It’s an eye. One eye. It’s not even a “generic cartoon round shape” eye. It’s shaped kind of like a normal eye. But there’s just one. Why?
I DON’T UNDERSTAND THE POOP WHY IS THE POOP A THING
A pager, a fax machine, a floppy disk, and a VHS tape. ‘Cause LOL 90’s, right?
I don’t even know what this is. What the hell is this?
Yup. Them’s shapes.
I think this last page is Android saying, “we don’t know what the hell category to put this stuff in, so here are drugs, a gun, an Easter Island head, and a toxic barrel, you goddamn Millennials.”
WHY DO YOU NEED ANY OF THESE IN PICTURE FORM. Why would I ever want to text message someone the high density polyethylene plastic recycling symbol? Why would I ever want to text someone die faces? Or chess pieces?
Or whatever the hell this thing is?
OR THE POOP?
Ugh.
Eigenblogger 