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.
The best things in life are pee. NO WAIT
Lists like this are dumb. Hell, I’m guilty of like 80% of these. Let’s rant.
1. Dressing for the weather.
When it’s -14 outside, I wear what’s practically a windbreaker and those tiny little thin gloves. Everyone else I see, including the dudes (SHOCKING!) are wearing appropriate clothing. So yeah.
2. Taking up the appropriate amount of space.
At least the author didn’t use the word “manspreading.” I like how manspreading gets all this hype about it, but nothing is said about the women who go on public transit with 3+ shopping/grocery bags and then just dump said bags into the seat next to them. How is that any better than a dude splaying his legs? I do the leg splay thing too, anyway, if I’m on the bus after a long walk. Only if it’s not crowded, though.
3.Taking care of themselves when they’re sick.
Nobody is good at taking care of themselves when they’re sick. Nobody. That’s why it sucks so hard. Story time: back in 2014 I got sick with what I’m assuming was some sort of Black Plague variant, ‘cause it completely knocked me for a loop (for those of you who don’t know: I very, very rarely get sick, but when I do, I feel like complete death). This was before I knew Nate, so I was basically on my own in my little basement apartment, trying not to die. I NEEDED medicine ‘cause my fever was approaching 104 and I was having trouble breathing because of the blood that was filling my lungs (exaggerating…or AM I?!), but the closest anything that sold anything of the sort was the Safeway a mile away. Let me tell you, man, I could BARELY make it to that Safeway. I thought my insides were going to catch fire, they hurt so bad. I almost had to ask some random person in Safeway if they would please drive me home, ‘cause I didn’t think I would make it the mile back. I did, I took meds, and was eventually fine, but seriously. Taking care of yourself when you’re sick is awful and no one is good at it.
4. Packing for trips.
Every guy I’ve ever known has been better than me at packing for trips. I take like 7 hours to get what I need ready and organized and packed. My guy friends grab their crap, chuck it into suitcases/backpacks, and are ready to go in like half an hour. And they never seem to forget anything, either.
5. Speaking at a volume that suits their current space.
You mean kids, not adult guys, right? Kids never speak at the appropriate volume. Adult guys do. F-.
6. Doing laundry in a way that doesn’t ruin at least one clothing item.
HAHA I GET IT IT’S A “WOMAN’S CHORE” SO GUYS SUCK AT IT AM I RIGHT?? Even if this were true for a dude (or a lady), I would suspect the growing pile of ruined clothes would prompt him (or her) to figure out how to freaking do laundry correctly.
7. Deciding when it’s time to get a haircut.
*old man voice* “I haven’t gotten a haircut since Truman was president and I’ll be dead and buried before these young whipper-snappers force me into a barber’s chair!”
8. Drying off after a shower.
THOG BIG MAMMOTH MAN! THOG CANNOT REACH BACK WITH TOWEL! THOG DO MANLY NAKED SPRINT THROUGH TOWN TO DRY OFF INSTEAD!
9. Communicating their feelings effectively.
NOPE NOPE NOPE NOPE NOPE NOPE NOPE
10. Sleeping in a position that doesn’t cause snoring.
Who can freaking control how they sleep once they’re asleep? I certainly can’t. I mean, I can fall asleep curled up on my side, say, but when I wake up I’m sprawled out on my back taking up the whole bed.
11. Waiting for their food to cool before they eat it.
THOG’S MOUTH ON FIRE, BUT THOG SO BAD AT COMMUNICATING HIS FEELINGS, HE CANNOT EXPRESS HIS DISTRESS AND PAIN!
12. Leaving the toilet seat up.
Really? Really?
13. Wearing matching socks.
Is this a serious issue for…anyone? I don’t think I’ve ever seen anyone wearing non-matching socks, unless it was deliberate. And even if a person does wear mismatched socks, who freaking cares?
14. Wearing properly fitting pants.
OH GOD, NOT IMPROPERLY FITTING PANTS!! Have you seen the ill-fitting pants that women wear? Have you? Have you seen MY pants? Not a single freaking one of them fits me “properly.” I think dudes are better at finding decent-fitting pants than the ladies are, honestly.
15. Knowing what looks good on their body type.
Wasn’t this covered in #14?
16. Being patient with someone who’s getting ready.
My dad is not patient with others getting ready. But does that generalize to all dudes? Nope! Not unless you do the same with one of my female friends, who can’t stand waiting for others.
17. Mansplaining.
I hate this word and I hate your face.
18. Zoning out when anything sports related is happening in the vicinity.
Goddamn home-wrecking sportsball, man. Does the zoning out include them zoning out on the sports as well? Like, if they suddenly flip to a football game on TV, do they just go into a fugue? That would actually be kind of hilarious. “THE PACKERS GAME IS ON THE RADIO; TURN IT OFF OR ELSE GARY’S GONNA DRIVE US INTO THE GRAND CANYON!”
19. Closing the shower curtain after a shower.
What? This is a thing that needs to be done? Shoot, I don’t do this either.
20. Empathizing about periods/childbirth.
I think they do the best they can, considering most guys never experience these things. It’s hard to empathize with something you can’t experience. When my mom is gagging from the smell of a skunk, for example, I can’t really empathize with that. I have no idea what that’s like, and I never will. So yeah.
21. Knowing when to stop talking.
Apparently the author of this article has the same problem!
Book Review: The Chosen (Potok)
Let’s review The Chosen today, shall we?
Have I read this before: I have, but I can’t remember when, exactly. High school, maybe?
Review: This is such a good book. Such an impactful book. I remembered a lot of this book from the first time I’d read it, and that’s saying something, especially considering I read it so long ago that I can’t actually remember when that was. I remember that the ending made me cry last time; it didn’t this time, but it was a very satisfying, complete ending, if that makes any sense. I don’t want to give away too much about this book, but if you’re looking for something thought-provoking that is super well-written and will stick in your brain for a while, read The Chosen.
Favorite part: This quote from Reuven’s father:
“Human beings do not live forever, Reuven. We live less than the time it takes to blink an eye, if we measure our lives against eternity. So it may be asked what value is there to a human life. There is so much pain in the world. What does it mean to have to suffer so much if our lives are nothing more than the blink of an eye? … I learned a long time ago, Reuven, that a blink of an eye in itself is nothing. But the eye that blinks, that is something. A span of life is nothing. But the man who lives that span, he is something. He can fill that tiny span with meaning, so its quality is immeasurable though its quantity may be insignificant.”
Rating: 7.5/10
Ten
So 2016 is just all about the milestones. Today, for example, marks exactly 10 years since I graduated high school. I’m not going to do a “here’s all the stuff that’s happened in the past decade” ‘cause I already did that for my decade blog anniversary (see this post), but it’s still a big deal in my opinion.
Ten years is a long time. A lot has changed, and most of it in ways I would have never expected. I certainly could have never predicted that at 28 I’d be living in Calgary, working on my second graduate degree, and engaged to be married.
I also wonder, every once and awhile, how all of these dorks are doing. I never talk to anyone from high school anymore.
Is your life something you would have never expected 10 years ago?
Week 23: The Wilcoxon Matched-Pairs Signed-Ranks Test
Yo! Today we’re going to talk about another nonparametric test: the Wilcoxon matched-pairs signed-ranks test!
When Would You Use It?
The Wilcoxon matched-pairs signed-ranks test is a nonparametric test used to determine if two dependent samples represent two different populations.
What Type of Data?
The Wilcoxon matched-pairs signed-ranks test requires ordinal data.
Test Assumptions
- The sample of subjects has been randomly selected from the population it represents.
- The original scores obtained for the subjects in the study are interval or ratio data.
- The distribution of the difference of the scores in the populations represented by the samples is symmetric about the median population difference score.
Test Process
Step 1: Formulate the null and alternative hypotheses. The null hypothesis states that in the two populations represented by the two samples, the median difference score between the two populations is zero. The alternative hypothesis claims otherwise (that the population median difference is greater than, less than, or simply not equal to zero).
Step 2: Compute the test statistic. The test statistic here is called the Wilcoxon T test statistic. Since the calculation is best demonstrated with data, please see the example shown below to see how this is done.
Step 3: Obtain the critical value. Unlike most of the tests we’ve done so far, you don’t get a precise p-value when computing the results here. Rather, you calculate your T test statistic value and then compare it to a specific value. This is done using a table (such as the one here). Find the number at the intersection of your sample size and the specified α-level. Compare this value with your T value.
Step 4: Determine the conclusion. If the calculated T value is larger than the table value, fail to reject the null hypothesis (that is, retain the claim that the samples do not represent different populations). If the calculated T value is equal to or smaller than the table value, reject the null hypothesis in favor of the alternative.
Example
The example for today’s test comes from one of the STAT 213 lab sections I taught last semester. I wanted to see if the students’ ranks in relation to their lab peers changed between midterm 1 and midterm 2. Set α = 0.05. The data is summarized in the following table, and an explanation of the columns can be found below.
H0: θD = 0
Ha: θD ≠ 0
Column 1 is the student ID.
Column 2 is the student’s ranks on midterm 1, with “1” corresponding to the student with the highest grade and “23” corresponding to the student with the lowest grade.
Column 3 is the student’s ranks on midterm 2, with “1” corresponding to the student with the highest grade and “23” corresponding to the student with the lowest grade.
Column 4 is the differences between the rank on midterm 1 and the rank on midterm 2.
Column 5 is the absolute values of Column 4.
Column 6 is the ranks of the values in Column 5. If a Column 5 value is zero, it is not ranked. If there are multiple identical values in Column 5, the average of their ranks is assigned to each of those values for Column 6.
Column 7 is the signed ranks of the values in Column 5. It is the same as Column 6, except if a value was negative in Column 4, its rank becomes negative in Column 7.
To obtain the Wilcoxon T test statistic, find the sum of the positive signed ranks and the sum of the negative signed ranks (all in Column 7). The absolute value of the smaller of these sums is the Wilcoxon T. Here,
So T = 99. The table value for a two-tailed test with n = 23 and α = 0.05 is 73. Since our calculated T is larger than the critical value, we fail to reject the null hypothesis and claim that the median difference in rank in the population is not different between midterm 1 and midterm 2.
Example in R
No R example this week, as this is probably easier to do by hand.
Eigenblogger 