Sunday, August 25, 2013

Things to put in waffles

Start with your basic waffle recipe (I use Bisquick mix)

Then add:

Candied walnuts
1/4 cup chopped walnuts
1/2 cup sugar
1/4 cup water
Place in sauté pan on medium heat and mix. Wait until sugar mix becomes dark caramel colored, but remove immediately if it starts to smell burnt. Pour walnut/sugar candy from pan and place on wax paper and allow to cool into chunk of hard candy. Chop into small pieces and add to waffle batter.

Blueberries for the adult who never learned to appreciate fruit chunks
1 cup blueberries
Whirr blueberries in food processor until they become a paste, then add to waffle batter.

Also add 1 cup of blueberries and a liberal handful of sugar to a skillet and heat slowly until the blueberries burst from the heat.  If your heat is too high you'll end up with candy from the burnt sugar instead of a sauce from the sugar mixing with the blueberries, if this happens just add some syrup to the skillet and the mix will return to something syrupy.  Only do this if you are kind-of OK with fruit chunks if enough sugar is involved.

Chocolate chips
1 cup chocolate chips

Cinnamon and sugar
1 tbsp cinnamon
2 tbsp brown sugar
2 tbsp dry waffle ingredients (either mix or flour)
Make waffles as usual but add an extra 2 tbsps dry ingredients and brown sugar and cinnamon.

Statistics Sunday: z score

Z score

So you know what percentile you are in if you are at 1, 2, or 3 standard deviations from the mean.

And just to be clear, you are in the .15%, the 2.5%, the 16%, the 84%, the 97.5%, or the 99.85%.

The z score is a standard deviation that is not ± 1, 2, or 3.  Or actually, it could be ± 1, 2, or 3, but it could also be any other number including non-whole numbers.  You can get the z score of a value with the formula z = (X-x̄) / σ.

The z score can then be used to tell you which percentile you are in by way of table.  There are lots of these tables available via Google, but here is one that is very readable and focuses on percentiles.

Sunday, July 7, 2013

Statistics Sunday: Standard deviation

So you sample a population a bunch of times and get a bunch of results, and those results cluster around the true mean of the population in a way that looks like a bell curve.

Say you know the true mean of a population:

To review, the mean is every value added together and then divided by the number  of values. The mean is often represented with the variable x̄.
  You can compare how different a study result is from the true mean by subtracting one from the other.
Technically this should be negative hair, but I wasn't sure how to show that.
This is called the deviation score, and is depicted by x.  Capital X represents an individual value, so in letters, the deviation score is x=X-x̄.

Why would you ever need a deviation score?  To calculate the variance!

The variance looks at how much a bunch of results deviate from the true mean.  It's a number value that describes having a thin, tall bell curve, where the results vary less (lower variance):

Or a short, fat bell curve, where the results vary more (higher variance):
So it would make sense to somehow add up the deviation scores to calculate the variance.  However, some of the deviation scores are positive and some are negative, so simply adding them up will give a result of 0.  One way math gets around this problem is to take the square of values that could be positive or negative before adding them up, then later taking the square root.  Because in math you can't just wave your hands and say, "Everything is positive!" 

So the variance takes the mean of the squares of the deviation scores, or [∑(x2)]/n.  The variance doesn't get around to taking the square root of that value, so it is represented as σ2.

The standard deviation does take the square root of that value, and so it is σ, or √{[∑(x2)]/n}.

The standard deviation has a special meaning when it comes to bell curves.

Being within 1 standard deviation of the mean represents 68% of all the values, being within 2 standard deviations of the mean represent 95% of all the values, and being within 3 standard deviations of the mean represents 99.7% of all the values.

And this is true for all bell curves.

So that's pretty useful.  But how you can use it is for another post.

Saturday, July 6, 2013

Shreveport Saturday: Water

Shreveport has a number of lakes around it.

Which can lead to some fun weekends.

Step 1: Make friends with someone with property or access to property around a lake.
Step 2: Make friends with someone who owns a boat.
Step 3:

There's lots of fishing to do around Shreveport, and the Bassmaster Tournament held every year on the Red River attracts family members to come visit us.

Other water attractions include the downtown fountains.

I haven't run through the fountains myself because I am too old to participate in such shenanigans.  Without a kid.  Which is why I may need to borrow a friend's kid some weekend this summer and supervise their playing in the fountains.  And then use them to go see Monsters University.

Sunday, June 30, 2013

Statistics Sunday: Bell curves

So you're doing a study on a population.

But you can't get everyone in America together and include them in the study, so you take a few people at random.

You hope that your study group is a good representation of the population as a whole, but it's possible to get a sample that is lopsided.

If your sample was chosen at random, you will more frequently get a study group that is similar to the population as a whole, and less frequently get a study group that is unlike the population as a whole.  Assuming you did a whole bunch of studies (and sampled the population a whole bunch of times), your results would look like a bell curve.

If your sample is larger, you are even more likely to get results closer to the true population.
And the bell curve reflects that.
If your sample is smaller, it is easier to get a lopsided sample.
And the bell curve reflects that too.

Saturday, June 29, 2013

Saturday Shreveport: Gardening

Did you know you can just plant things in the ground and they will survive?

I started my vegetable garden a little late in the year, which was good because I missed all the surprise frost at the end of spring, but I don't have a lot of vegetables yet.

I started some plants as seeds indoors (jalapeños, bell peppers, tomatoes, basil) in early March and some as seeds outdoors (cucumbers, bok choy, cilantro, and a "mixed lettuce" seed packet) in late April, when I planted my seedlings from indoors.  For the first week of seeds I convinced myself that nothing was ever going to actually appear out of the soil, but except for the Unexplained Great Basil Loss of early April every plant has survived in some form.

So far I've gotten a decent (aka, I will never be able to eat this by myself before it goes bad) amount of lettuce.  I read that lettuce likes cold weather so I thought seeding it in April would ensure it would go terribly, but it actually managed to produce enormous leaves before it went to seed/got taken over by the cucumbers.  I thought maybe producing my own food could cut down on the grocery bill (I certainly haven't had to buy lettuce in weeks), but instead it's remained the same because salad dressing and toppings cost about as much as our regular groceries.

Excitingly, although no fruit has grown yet, the cucumber, tomatoes, and bell peppers/jalapeños are flowering.  (I lost track of what's a bell pepper and what's a jalapeño plant, so whatever produces fruit will be a surprise.)

I had dreams of picking cilantro out of the garden all summer (we use a lot of cilantro in cooking), but now that it's big enough that breaking off handfuls probably won't kill the whole plant it's going to seed.  (I guess we'll have plenty of coriander?)  On the other hand, the cucumbers are taking over the entire garden and part of the yard.  I might try to give them more surfaces to climb than the fence, but the stems are a little prickly and I'm not sure how well this is going to go for my arms.

Not shown: the corner of the planting bed that's been given over entirely to weeds.
I don't have much of a green thumb (see: last August when I forgot to water all my potted plants for the entire month), but it helps to have lots of plants so when some go kaput it seems like a less impressive failure.

Sunday, June 23, 2013

Statistics Sunday: Errors and Not-Errors

So, this:

In any study's conclusion, you would either accept the null hypothesis and reject the alternate hypothesis, or you would accept the alternate hypothesis and reject the null hypothesis.  

Therefore, you have a 50% chance of your study being right or wrong.  The end.  You're welcome for this explanation of all of statistics.

Just kidding.

So, let's say you reject the null hypothesis and accept the alternative hypothesis.

If you are wrong, you have accepted the alternative hypothesis when it is false.  This is called either a false positive or Type I error.  The probability that you have done this is called α, which is the same thing as the p-value.  There are two letters that denote the same value because it makes statistics more funner. (Grammar joke!)

Or, you could accept the null hypothesis and reject the alternate hypothesis.
If you are wrong, you have rejected the alternative hypothesis when it is true.  This is called a false negative or Type II error.  The chance that you have done this is β.  To have a good study, you want the β to be ≤ 0.2, or less than a 20% chance that a true alternative hypothesis is rejected.

So to review:

These values represent the probability of errors occurring: 
α or p-value: probability that false alternative hypothesis is accepted (Type I error)
β: probability that true alternative hypothesis is rejected (Type II error)

But what if this happens:
And you are right?  A false null hypothesis has been rejected.  The probability of this happening is called the power, and is 1-β.  Instead of talking about the β of a study, people usually talk about the power since it provides the same information.  The power of a study should be ≥ 0.8, or provide a greater than 80% chance of rejecting a false null hypothesis, as this will also provide an acceptable β.

So there must be one more value to talk about.  You do this:
And you are correct.  The true null hypothesis has been accepted.  This is 1-α.  In studies, no one cares about this value so it doesn't have a name that is used frequently in conclusions of papers.  People simply talk about the p-value because it is α and relates closely to 1-α.  Womp, womp.

So in conclusion:

These values represent the probability of errors occurring: 
α or p-value: probability that false alternative hypothesis is accepted (Type I error)
β: probability that true alternative hypothesis is rejected (Type II error)

These values represent the probability of errors not occurring:
power: probability that false null hypothesis is rejected (1-β)
_____: probability that true null hypothesis is accepted (1-α)

Studies usually use only p-value and power to describe all four of these probabilities.  A better p-value will mean a better 1-α, and a better power will mean a better β.  A good p-value is < 0.05, and a good power is > 0.8 .