Introduction to Statistics for the Social Sciences - PowerPoint Presentation

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Introduction to Statistics for the Social SciencesSBS200 - Lecture Section 001, Spring 2019Room 150 Harvill Building9:00 - 9:50 Mondays, Wednesdays & Fridays.

http://www.youtube.com/watch?v=oSQJP40PcGI

March 20

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Even if you have not yet registered your clicker you can still participate

The

Green

Sheets

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Before next exam (April 5th)Please read chapters 1 - 11 in OpenStax textbookPlease read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

Schedule of readings

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Lab sessions

Everyone will want to be enrolled

in one of the lab sessions

Labs continue this

week

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Standard

deviation and Variance For Sample and Population

These would be helpful to know by heart – please memorize

these formula

Pop

Quiz

Question

1

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Standard

deviation and Variance For Sample and Population

Pop

Quiz

Question 1

Question 2:

Please draw two curves and include critical values for one-tailed test versus a two-tailed test

Question 3:

When we move from a two-tailed test to a one-tailed test the critical z score gets _____ (bigger or smaller?)

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Question 4:

If we use a one-tailed test and the prediction is correct, then it is ____ (easier, harder or impossible) to reject the nullQuestion 5: If we use a one-tailed test and the prediction is incorrect, then it is ____ (easier, harder or impossible) to reject the nullQuestion 6: When do we use a t-test and when do we use a z-test?        (Be sure to write out the formulae)

Pop

Quiz

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Standard

deviation and Variance For Sample and Population

Pop

Quiz

Question 1

Question 2:

Please draw two curves and include critical values for one-tailed test versus a two-tailed test

Question 3:

When we move from a two-tailed test to a one-tailed test the critical z score gets _____ (bigger or smaller?)

1.64

Critical value gets smaller

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Question 4:

If we use a one-tailed test and the prediction is correct, then it is ____ (easier, harder or impossible) to reject the nullQuestion 5: If we use a one-tailed test and the prediction is incorrect, then it is ____ (easier, harder or impossible) to reject the nullQuestion 6: When do we use a t-test and when do we use a z-test?        (Be sure to write out the formulae)

Pop Quiz

easier to reject

impossible to reject

Population versus sample standard deviation

Population versus sample standard deviation

Use the t-test when you don’t know the standard deviation of the population, and therefore have to estimate it using the standard deviation of the sample

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.

.

A note on z scores, and t score:

Difference between means

Variability

of curve(s)

Difference between means

Numerator is always distance between means

(how far away the distributions are or “effect size”)

Denominator is always measure of variability (how wide or much overlap there is between distributions)

Variability of

curve(s

)

(within group variability)

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.

Effect size is considered relative

to variability of distributions

1. Larger variance harder to find significant difference

Treatment

Effect

Treatment

Effect

2. Smaller variance easier to find significant difference

x

x

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Effect size is considered relative

to variability of distributions

Treatment

Effect

Treatment

Effect

x

x

Variability of curve(s)

(within group variability)

Difference between means

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.

A note on variability versus effect size

Difference between means

Variability

of curve(s)

Variability of curve(s)

(within group variability)

Difference between means

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.

.

Difference between means

Variability

of curve(s)

Variability of curve(s)

(within group variability)

Difference between means

A note on

variability

versus effect

size

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.

Hypothesis testing: A review

If the observed stat is more extreme than the critical stat in the distribution (curve): then it is so rare, (taking into account the variability) we conclude it must be from some other distribution decision considers effect size and variability then we reject the null hypothesis – we have a significant result then we have support for our alternative hypothesis p < 0.05 (p < α)

If the observed stat is NOT more extreme than the critical stat in the distribution (curve): then we know it is a common score (either because the effect size is too small or because the variability is to big) and is likely to be part of this null distribution, we conclude it must be from this distribution decision considers effect size and variability – could be overly variable then we do not reject the null hypothesis then we do not have support for our alternative hypothesis p not less than 0.05 (p not less than α) p is n.s.

Variability of curve(s)

Difference between means

critical statistic

critical statistic

Variability of curve(s)

Difference between means

Variability of curve(s)

(within group variability)

Review

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The central limit theorem states that, for any distribution, as n gets larger, the

variability of the sampling distribution of the sample mean _______. a. becomes largerb. becomes smallerc. is closer to a normal distributiond. is closer to the standard deviation

Let’s try one

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Mark and Melvin work inside Intel's semiconductor fabrication plants.

In

these “clean rooms” the workers wear "bunny suits". Mark and Melvin are each assigned a different team to measure the workers. Both teams measure the same sample of 100 workers and determine the very specific dimensions of their “bunny suits”. Mark spends a week training his team of data collectors, providing identical tape measures and creating a strict protocol for measuring the workers. Melvin however, simply sends out his team to measure the workers, with little instruction, and consequently Melvin’s workers make many more mistakes in recording the data, and the data are more variable. How would you explain the difference in variability between the two groups? The difference in variability between these two group is due to:a. the difference in sample size, because as sample size increases variability decreasesb. differences in the population, because if the population is more variable, the sample will be more variablec. differences in the amount of random error in the two samples, because as random error increases so will variabilityd. all of the above are reasons why Melvin’s data are more variable than Mark’s

Let’s try one

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Let’s try one

Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?

a. the means are the same, so the t-test would yield the same results.b. the means are the same, but the variability would increase so it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so it would be easier to reject the null hypothesis.

correct

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Let’s try one

Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?

a. the variance would get bigger and the confidence interval would get wider

b. the variance would get bigger and the confidence interval would get narrowerc. the variance would get smaller and the confidence interval would get widerd. the variance would get smaller and the confidence interval would get narrower

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Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?

a. the means are the same, so the t-test would yield the same results.b. the means are the same, but the variability would increase so it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so it would be easier to reject the null hypothesis.

correct

Let’s try one: Just for fun

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Ho: µ = 5

Ha: µ ≠ 5

Bags of potatoes from that plant are not different from other plants

Bags of potatoes from that plant are different from other plants

Two tailed test

(

two-tailed

α = .05)

1.96

1

16

√

= .25

z = 4.0

1.96

-1.96

1

4

=

z-score : because we know the population standard deviation

6 – 5

.25

= 4.0

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Yes

Yes

Yes

These three will always match

Probability of Type I error is always equal to alpha

Because the

observed z (4.0 ) is bigger than critical z (1.96)

1.64

No

Because observed z of 4

is still bigger than critical z of 1.64

2.58

there is a difference

No

Because observed z of 4 is still bigger than critical z of 2.58

there is no difference

there is not

there is

1.96

2.58

0.05

Lecture ended here

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Two tailed test

(α = .05)

Critical t(15) = 2.131

t- score : because we don’t know the population standard deviation

n – 1



16 – 1 = 15

2.13

-2.13

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Two tailed test

(α = .05)

Critical t(15) = 2.131

89 - 85

6

16

√

2.667

t- score : because we don’t know the population standard deviation

n – 1



16 – 1 = 15

2.13

-2.13

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Yes

Yes

Yes

These three will always match

Probability of Type I error is always equal to alpha

.05

Because the

observed z (2.67) is bigger than critical z (2.13)

1.753

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Yes

Yes

Yes

.05

1.753

No

Because observed t

(15) = 2.67 is still bigger than critical t(15) of 1.753

2.947

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Yes

Yes

Yes

.05

1.753

No

Because observed t

(15) = 2.67 is still bigger than critical t(15) of 1.753

2.947

consultant did improve morale when in fact she did not improve morale

Yes

Because observed t(15) = 2.67 is not bigger than critical t(15) of 2.947

consultant did not improve morale when in fact she did improve morale

2.131

2.947

No

No

No

These three will always match

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The average weight of bags of potatoes from this particular plant

is 6 pounds, while the average weight for population is 5 pounds.

A z-test was completed and this difference was found to be statistically significant. We should fix the plant. (z = 4.0; p<0.05)

Start summary with two means (based on DV) for two levels of the IV

Describe type of test (z-test versus t-test) with brief overview of results

Finish with statistical summaryz = 4.0; p < 0.05

Or if it *were not* significant:z = 1.2 ; n.s.

Value of observed statistic

n.s

. = “not significant”

p<0.05 = “significant”

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The average job-satisfaction score was 89 for the employees who went

On the retreat, while the average score for population is 85. A t-test

was completed and this difference was found to be statistically

significant. We should hire the consultant. (t(15) = 2.67; p<0.05)

df

Value of observed statistic

n.s

. = “not significant”

p<0.05 = “significant”

Start summary with two means (based on DV) for two levels of the IV

Describe type of test (z-test versus t-test) with brief overview of results

Finish with statistical summary

t(15) = 2.67; p < 0.05

Or if it *were not* significant:

t(15) = 1.07;

n.s

.

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Thank you!

See you next time!!