Sampling distribution blog

The sampling distribution is the “theoretical probability distribution of all possible sample values for the statistics in which we are interested” (Frankfort-Nachmias & Leon-Guerrero, 2015, p. 219). Since this includes every possible combination of units in a sample, the sampling frame can become fairly enormous for even small samples – thankfully, it’s mainly theoretical, and rarely calculated. This sampling distribution, for whatever statistic it’s calculated for, can be described like other distributions with mean and standard deviation, which is referred to as the standard error of the mean in this context. Conclusions drawn from these concepts serve as the basis for inferential statistics.

While largely theoretical, sampling distributions have important implications on sampling techniques and generalizability. For example, the larger the sampling frame becomes (or, in other words, the larger the sample size), the more the sampling distribution begins to resemble a normal distribution – this is known as the central limit theorem. This means that the larger the sample, the more likely that sample’s mean is to match the actual population mean. Since the goal of inferential statistics is to infer a statistic about an entire populated out of sample data, this theorem serves as the basis for inferential statistics.

https://www.youtube.com/watch?v=Zbw-YvELsaM

This video introduction explains the concept of a sampling distribution, through an intentionally contrived example of a professor who wants to know the average age of a college class, but is unable to sample more than three students at a time. It serves as a good introduction to sampling distributions for the uninitiated, but I wanted to draw attention to it because I really like the ending thoughts.

The textbook and the video both answer the question of why the reader/viewer should care in the same way, but they do so in different ways. The video highlights the ability of sampling distributions to quantify the likelihood of a sample statistic accurately reflecting the population statistic – it’s both really cool that one is able to do this, and really important in that it allows one to provide a metric of generalizability for statistics calculated from a given sample. Of course, this is all implied by the textbook’s thorough explanation of the central limit theorem, but the textbook probably doesn’t spell it out this way since this is part of the next chapter topic.

 

Data analysis blog

I’m also certainly deeply misinterpreting the blog topic this week, but our task in this blog assignment is to develop two research questions that can be operationalized using variables in our class SPSS datasets, and to examine them using the data analysis techniques presented in chapters two and three. This is excessively difficult, as none of the techniques that we’ve covered so far focus on bivariate comparison, and a research question must have at least two variables in order to derive a hypothesis from it (a possible exception: some graphs that we covered could allow for meaningful bivariate comparisons if both variables are measured at the interval-ratio level). This would lead to an extraordinarily tedious blog, where I graph and elaborate upon two disconnected dichotomous variables, which are perhaps better expressed in ten words or less.

 

However, while chapter two doesn’t touch upon how to construct a table with more than one variable in it, it does devote a rather lengthy section on interpreting these tables. Therefore, I’m going to risk my grade, and suggest that crosstabs are valid in this blog. Also, if bivariate analysis is disallowed, I couldn’t possibly “examine” either research question, so it’s arguably a risk either way.

 

My preference is to develop a broad research question that can be asked in two ways. Using a structuralist perspective, one might think that political beliefs and values pattern other political beliefs. Therefore, I’m curious in:
RQ1: Does tolerance of premarital sex predict support of abortion?

RQ2: Does confidence in medicine predict support of abortion?

 

Three relevant variables are found in our 2010 GSS subset: conmedic, abany and premarsx.

 

Abany:

Question text: Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion . . .If the woman wants it for any reason?

Possible responses: Inapplicable, Yes, No, Don’t know, No answer

 

Conmedic:

Question text: I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say you have a great deal of confidence, only some confidence, or hardly any confidence at all in them? Medicine

Possible responses: Inapplicable, A great deal, Only some, Hardly any, Don’t know, No answer.

 

Premarsx:

Question text: There’s been a lot of discussion about the way morals and attitudes about sex are changing in this country. If a man and woman have sex relations before marriage, do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?

Possible responses: Inapplicable, Always wrong, Almost always wrong, Sometimes wrong, Not wrong at all, Don’t know, No answer.

 

Below are the results of the crosstab analysis:

 

 

 

ABORTION IF WOMAN WANTS FOR ANY REASON * SEX BEFORE MARRIAGE Crosstabulation
Count
  SEX BEFORE MARRIAGE Total
ALWAYS WRONG ALMST ALWAYS WRG SOMETIMES WRONG NOT WRONG AT ALL
ABORTION IF WOMAN WANTS FOR ANY REASON YES 16 6 23 124 169
NO 107 30 48 115 300
Total 123 36 71 239 469

 

 

ABORTION IF WOMAN WANTS FOR ANY REASON * CONFIDENCE IN MEDICINE Crosstabulation
Count
  CONFIDENCE IN MEDICINE Total
A GREAT DEAL ONLY SOME HARDLY ANY
ABORTION IF WOMAN WANTS FOR ANY REASON YES 75 95 11 181
NO 107 138 33 278
Total 182 233 44 459

 

The results are mixed. Strong convictions against sex before marriage definitely have some degree of correlation with strong convictions against abortion, but the relationship kind of falls apart after that. Beyond this curious relationship, I’m not sure I see many opportunities for further research based off of these results. However, that relationship does suggest that there might be a superior variable, or combination of variables, to predict support of abortion.

 

SOCY 508 Introduction

Hi everyone! I’m Peter Jameson, and this is my second semester in the sociology program at VCU. I also did my undergraduate work in political science here. My experience with statistics is limited, since my undergraduate program didn’t require me to actually take a statistics course. I have taken an undergraduate research methods course, as well as SOCY 601, so I think I’m somewhat familiar with a few of the concepts that we’ll be discussing, but I can see that there’s still a lot more to learn just by flipping through the textbook. I’m definitely not the most mathematically oriented person, but I’m really looking forward to working on the SPSS exercises. I took an online introductory course in R last year, and I have a lot of experience in bash and Python, so I’m hoping that I’ll click with SPSS.

In any case, this is largely just a test post to make sure it gets picked up by the class page, but I think there are two or three other introductory posts for other classes on this page, and if you’d like to chat about anything in particular, feel free to comment!

 
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