I have two questions I am stuck on for this assignment.
- Address Margin of Error for categorical vs numeric data.
The other is:**
- Address the size of Margin of Error as compared to the appropriate measure of Central Tendency. (Mean for numeric data & proportion for categorical data)
If anyone has some insight, or websites that I can look at to get this information, it would be greatly appreciated.
Okay, well I figured out the first one after doing some digging, but after researching all day yesterday, and for several hours today, I still can’t figure out the second question:
• Address the size of Margin of Error as compared to the appropriate measure of Central Tendency. (Mean for numeric data & proportion for categorical data)
Maybe I’m not understanding the question though.
100 views, can anyone help?
Not if you don’t post enough information for people to understand what you’re asking.
If you don’t mind asking what other information you need, I can try my best to provide.
That was the only information I was given to complete the assignment.
I think the confusion may be due to not enough information given on the professors part, 125 people can’t even understand it on here.
The only info I have is:
It’s a level 1 statistics course
We were give this question to answer:
Address the size of Margin of Error as compared to the appropriate measure of Central Tendency. (Mean for numeric data & proportion for categorical data)
I THINK he’s asking to talk about the size of the margin of error when you have a mean or when you have a proportion.
But that’s the best I can do.
Any ideas or other questions?
It looks to me like your instructor is asking you to discuss the meaning of two terms (Margin of Error and Central Tendency) by comparing them. He has even capitalized the words to draw attention to them (or was that you?) In any case, I’m guessing you were supposed to have learned these terms and he wants you to demonstrate that knowledge. What I tell my son: reread the chapter.
Ah, that might make sense.
I’ll do that.
I think the majority of my confusion is in the way the question is worded.
Does “margin of error” mean “standard deviation?” If so, standard deviation for a sample is calculated differently for categorical (proportion) and numerical (mean) data.
No, margin of error refers to the sampling error. Sample standard deviation will have sample error as a component, but every population has a standard deviation. The professor’s question asks the student to discuss the size of the sampling error compared the the measure of central tendency – the mean for numerical data, the mode for categorical data (I see the professor uses “proportion” as the measure for categorical data – that’s going to affect the discussion; I don’t see proportion as a measure of central tendency, so the contrast will be considerable).
As a statistics instructor, I can say that this question is worded terribly. The proportion is not a measure of central tendency. The mean and the median are measures of central tendency, with the mean differing from the median in skewed distributions.
Now, if your instructor is talking about the means of sampling distributions, then the mean of the sampling distribution of the ordinary sample proportion is the true proportion (I’ll call it p). The (true) standard error is then s.e.= sqrt(p(1-p)/n), with n the sample size. Typically, the sample proportion is substituted into this expression, because we don’t know p.
In most introductory stats classes, the margin of error for a sample proportion given is the “large-sample” one, which is z*s.e., where z is some quantile from the standard normal distribution.
Similarly, the mean of the sampling distribution of the sample mean is mu, and the standard error is sigma/sqrt(n). Since we typically don’t know sigma, we typically use s.e. = s/sqrt(n), with s the sample standard deviation. The margin of error is then t*s.e., where t is some quantile from the Student’s t distribution.
The proportion is the mean of indicators. That’s not to say that the question isn’t poorly worded–it is–but it’s not at all nonsensical.
Since the OP mentioned it was a low-level stats class, I assumed indicator variables weren’t discussed. If it’s anything like the one I teach (a coordinated course that I have no say in by the way), it barely even covers the binomial, and doesn’t discuss it as the the sum of indicators.
ETA: Another reason I eschewed the topic of indicators is that it would make the original question redundant. The OP’s instructor is making the distinction between mean and proportion explicit in the question (“mean for numeric data and proportion for categorical data”), so it seems that the instructor wants to separate the two (although, of course, the proportion is a special kind of mean, for 0/1 data).