Transcription
What is going on wonderful people? It's Medicosis Perfectus, where medicine makes perfect sense. Welcome back to my statistics playlist. In this video, we shall define many terms, including: what is the population? What's the definition of the sample? What is a parameter in statistics? And what is a statistic? Let's find out.
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"There are three kinds of lies," said Mark Twain, "lies, damned lies, and God damn statistics." Welcome to my statistics playlist. Make sure to save this playlist if you wish to converse with me. "Mother, dear," said Voltaire, "define your terms." Here are the terms that we shall define today: population, sample, parameter, and a statistic. And what better way to define our terms than by using a Socratic dialogue: question and answer. So, let's start with this case.
A researcher wants to know what percent of all households in Toronto have a single male as the head of the household. The researcher conducted a survey with 400 households and established how many of these households are headed by a single male. In this case, what is the population? Is it A, the total population of the world? B, the total population of Canada? C, the total population of Toronto? D, all the households of Toronto? E, the 400 households selected? F, the percentage of households headed by a single male in Toronto? Or G, the percentage of households headed by a single male among the 400 households selected? Please pause.
Okay, so what is the population? As far as statistics is concerned, basically, you need a numerator and a denominator. The population is your denominator. So, which denominator should I select in this particular case? Okay, begin with the end in mind. What are we trying to find out? We're trying to find out the percent of all households in Toronto that have a single male as the head of the household. So, what should be the numerator? Number of households in Toronto with a single male head of household. And what should be the denominator? The answer is all the households of Toronto. Out of all of the households of Toronto, how many of which are headed by a single male? So, the correct answer for the population is Choice D, as in doofus.
The second question is, in the same case, what is the sample? Is it A, B, C, D, E, F, or G? Please pause the video and try to answer this yourself. Why do we need a sample in statistics? Because we do not have the time, or the energy, or the money to interview all of the households in the city of Toronto. So, to maintain our sanity, we're going to choose a random sample that is representative of the population of Toronto. And this sample will contain only 400 households out of all of the households of Toronto. So, my sample is the 400 households selected, which is Choice E.
The third question is, in the same case, what is the statistical parameter? Is it A, B, C, D, E, F, or G? Please pause the video. In brief, the parameter is what you're looking for. And I'm looking for the percent of all the households in Toronto that have a single male as the head of the household. So, the correct answer is Choice F, as in F me.
Fourth, in the same case, what is the statistic? The statistic is, is it A, B, C, D, E, F, or G? Please pause the video. The correct answer here is the statistic is the percentage of the households headed by a single male among the sample selected. So, the parameter is among the entire population, but the statistic is among the selected sample. The parameter is for the many, whereas a statistic is for the few.
To belabor this point, because it's worth belaboring: this is the sample. The sample had 400 total households in Toronto out of, let's say hypothetically, 1 million total households in the city of Toronto. After we have interviewed all of these kind souls, we realize that only 40 out of 400 households are headed by a single male, which gives me a ratio of 10% or 0.1. And assuming that our sample was representative and random, we can infer onto the total population, who has 1 million total households, that 10% of the 1 million are headed by a single male. So, therefore, 10% of 1 million is how much? It's 100,000. So, we have 100,000 households in the city of Toronto headed by a single male out of the million total households. And that's the beauty and the danger in statistics. That you do not have to interview every single one of them. You can just take a random representative sample and then infer. If your sample is truly random and truly representative, then you can safely infer, and your results will tend to be more accurate than not.
The problem is that in today's world of dude bros and douche canoes, people are so lazy, and the random is rarely representative, let alone random. So, you end up simply interviewing your buddies, and you find that 60% of these households are headed by a single male. But in reality, your sample has nothing to do with real life. And we get deep into the mud when these dude bros are later going to advise government officials, who themselves cannot find their gluteus maximus with both hands if their life depended on it.
If you wish to see more videos like this in the future, please drop your favorite math symbol in the comments. So, 40 to 400 in the sample is equivalent to 100,000 to a million in reality. 10% and 10%. This jump is called a statistical inference.
Now, let's define our terms to please Voltaire. Where's the sample? Where is my population? The million is my population. Where's the sample? 400 is my sample. What is the statistic? Stat. Statistic is the part. 10% that's the sample. What is the parameter? That's the whole. That's the many, not the few. Also 10%. This is what I'm trying to achieve and figure out, and this is the shortcut that I had to take in order to infer from that what I wanted to achieve.
Boring definitions: The population is the entire group you're interested in studying. The sample is the subset drawn from the entire population that you're interested in studying. If parameter is a certain characteristic of the population (e.g., how many of them are headed by a single male), and the statistic is a number describing some characteristic that you calculate from the sample data, then we're going to use the statistic to estimate the parameter. That was deep.
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