Feb 27 2012

SOC202

Two group difference of means test:

A lot of people in Canada compared to are neither believers nor non-

believers.

Non-believer and believer: do these two groups have the same or

different levels of distress?

•Imagining another table that has believers and their level of

distress (mean) and compare it to non-believers, we should be

able to see if the relaxed got hypothesis is true, then believers

should have lower distress.

•Null hypothesis, in the sample of which this population was

drawn, there is no difference in mean level of distress

•Operationalization of distress: The distress index that is used in

the research analysis paper

Cases drop off - people who didn't answer the distress items are not in

the issue.

People forget that this is all estimates. Nothing is precise. Thing to

keep in mind is comparison and estimate.

•Look for example to refute null hypothesis

•Two tail test means, rather than suggesting a direction, let's just

say there is a difference. it could be this way, or it could be the

other way.

•Means are just one part of the story. another part of the story is

variance.

•Ideal is, you want believers and non believers to be far apart.

You don't want a lot of spread between groups. if u ave believers

here and non believers in other side in an index, far apart and

uniformity within

Imagine that at some point u have to almost hypothetically, sample

after sample, scooping up if null hypothesis is true, if its close to zero,

just plot it on frequency distribution.

Just like the dice example in the book, if you scoop up a population and

it gives you a big difference, something is wrong, or null hypothesis is

false.

It's like taking that dice example and pulling that to the example prof

Feb 27 2012

SOC202 Quantitative Analysis in Social Sciences

SP.TG.

Page 1

gave. How likely is it get to 2 or a 12 rolling 2 dice? Very little.

Ideal: bigger difference between means.

Believers have a bit, but not much. But it'll be statically significant

because the sample population is large.

Instead of getting 60 000, if we did a study of 500 canadians, these

kinds of SD will be hard to reach a statically significant effect.

In larger samples, gives you a more flexibility to have larger variation.

Versus smaller samples, there are greater fluctuations around the

average.

Prof wants to be able to talk about the bigger difference between the

means (eg. this group is different from the other group, and there is

small variance etc (you want SD to be somewhat similar))

T-statistic: here's the centre, t-statisitic that you would get if null

hypothesis is true, is zero. You're building a case against the null

hypothesis.

The numerator (test effect) in the case against the null is the

difference between the two means.

Denominator is the standard error. It is the pooled variance estimate.

Sample to sample to sample variability is the pooled variance.

The whole idea here is, t-statistic is 'test error divided by standard

error'

p-value the tee will set is .05. We'll say it is a two-tailed test (Believers

could be better off, or not better off).

Null hypothesis is in the middle.

The interpretation:

On average, people who agree or strongly agree with the statement

"the challenges i face in lfe are god sway of testing me" report a higher

level of distress compared to study participants who reject or deny this

statements.

There is a real difference in the levels of distress b/w believe era and

non believers

* highly unlikely the that observed difference of .618 resulted from

normal, expected from sampling error. Statistically speaking, it is

different enough from expected, from giving a confidence that this isn't

a fluke.

* It doesnt stay whether a difference is big enough to make a big deal

about it

Feb 27 2012

SOC202 Quantitative Analysis in Social Sciences

SP.TG.

Page 2

Repeated sampling - established level of distress and take their

diffference

•In repeated sampling, it will cluster around zero.

•Down the side, the t-statistic work out in a different cvalue of

freedom. You can see difference between 20 and infinity is not

that big.

•If the null is true, it will be near zero.

•Pulling out a sample from below, is not likely to happen if

difference is zero. How likely? P-value

•Sampling distribution of a large number of sampling mean

differences in a symmetrical and centers on zero

•This is consistent: people who attend regularly seems beneficial

to them. Gives them support. They have lower levels of distress.

You don’t have to memorize the Standard Error of Difference between

two means formula, but know key points from slides.

•Look at the mean for one group and other for second, see how

big is the spread

•Other idea: “heteroscedasticity” is about legal variances – griup

2 = ow variance (want equal variances)

•You don’t want G1 to have large variance and group 2 have

small

Degree of Freedom: It is basically taking n into account and basically

says bigger the sample, the better – that’s the basic idea. The standard

error will be lower that way.

You want large difference in the mean (case against the null) – it

standardizes difference between the mean

“What happens to me in the future mostly depends on god”: look at

the size of test effect and standard error is larger.

T-statistic is 1.111 (much smaller) since numerator is smaller and

denominator is larger.

p-value .227 (greater than .05 so it fails to reject the null hypothesis)

By hand, if someone gave you a t-stat, how do you know its p-

value/whether it rejects null hypothesis? -> 1.96 is the value!!

Feb 27 2012

SOC202 Quantitative Analysis in Social Sciences

SP.TG.

Page 3

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###### Document Summary

A lot of people in canada compared to are neither believers nor non- believers. Cases drop off - people who didn"t answer the distress items are not in the issue. Ideal is, you want believers and non believers to be far apart. You don"t want a lot of spread between groups. if u ave believers here and non believers in other side in an index, far apart and uniformity within. Imagine that at some point u have to almost hypothetically, sample after sample, scooping up if null hypothesis is true, if its close to zero, just plot it on frequency distribution. Just like the dice example in the book, if you scoop up a population and it gives you a big difference, something is wrong, or null hypothesis is false. It"s like taking that dice example and pulling that to the example prof. But it"ll be statically significant because the sample population is large.

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