Lecturer’s desk INTEGRATED LEARNING CENTER ILC 120 Screen 11 10 2 1 98 7 6 5 13 12 15 14 17 16 19...

Lecturer’s desk

INTEGRATED LEARNING CENTER ILC 120

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brokendesk

Introduction to Statistics for the Social Sciences

SBS200, COMM200, GEOG200, PA200, POL200, or SOC200Lecture Section 001, Fall, 2014

Room 120 Integrated Learning Center (ILC)10:00 - 10:50 Mondays, Wednesdays & Fridays.

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

Reminder

A note on doodling

Schedule of readings

Before next exam (November 21st)

Please read chapters 7 – 11 in Ha & Ha

Please read Chapters 2, 3, and 4 in PlousChapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight BiasChapter 4: Context Dependence

Homework due – Wednesday (November 12th)

On class website: Please print and complete homework worksheet #19

Using Excel for hypothesis testing with ANOVAs

Labs continue this week with Project 2

(with the exception of Tuesdays labs)

By the end of lecture today 11/10/14

Use this as your study guide

Hypothesis testing with Analysis of Variance (ANOVA)Constructing brief, complete summary statements

Study Type 2: t-test

Study Type 3: One-way Analysis of Variance (ANOVA)

Comparing more than two means

We are looking to compare two means

Single Independent Variable comparing more than two groups

Study Type 3: One-way ANOVA

Single Dependent Variable (numerical/continuous)

Independent Variable: Type of incentiveLevels of Independent Variable: None, Bike, Trip to Hawaii

Dependent Variable: Number of cookies soldLevels of Dependent Variable: 1, 2, 3 up to max sold

Between participant designCausal relationship: Incentive had an effect – it increased sales

Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and looked to see whosold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bikeor 3) Nothing. This is an example of a true experiment

Used to test the effect of the IV on the DV

How could wemake this a

quasi-experiment?

Single Independent Variable comparing more than two groups

Study Type 3: One-way ANOVA

Single Dependent Variable (numerical/continuous)

Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and looked to see whosold more cookies. The 3 incentives were 1) Trip to Hawaii, 2) New Bikeor 3) Nothing. This is an example of a true experiment

Used to test the effect of the IV on the DV

None New Bike

Sale

s per

Gir

l sc

out

TripHawaii

None New Bike

TripHawaii

Dependent variable is

always quantitative

In an ANOVA, independent variable is qualitative

(& more than two groups)

Sale

s per

Gir

l sc

out

Be careful you are not designing a Chi Square

One-way ANOVA versus Chi Square

None New Bike

Sale

s per

Gir

l sc

out

TripHawaii

This is an ANOVA

None New Bike

Tota

l N

um

ber

of

Box

es

Sold

TripHawaii

This is aChi Square

If this is just frequency you may have a

problem

These are

means

These are

means

These are

means

These are just frequencies



One-way ANOVA

One-way ANOVAs test only one independent variable- although there may be many levels

“Factor” = one independent variable “Level” = levels of the independent variable

• treatment• condition• groups

“Main Effect” of independent variable = difference between levels • Note: doesn’t tell you which specific levels (means) differ

from each other

A multi-factor experiment would be a multi-independent variables experiment

Number of cookies sold

Incentives

None Bike Hawaii trip

Comparing ANOVAs with t-tests

Similarities still include:

Using distributions to make decisions about common and rare events

Using distributions to make inferences about whether to reject the null hypothesis or not

The same 5 steps for testing an hypothesis

The three primary differences between t-tests and ANOVAS are:1. ANOVAs can test more than two means2. We are comparing sample means indirectly by

comparing sample variances3. We now will have two types of degrees of freedom t(16) = 3.0; p < 0.05 F(2, 15) = 3.0; p < 0.05

Tells us generally about number of

participants / observations


participants / observations


groups / levels of IV

A girlscout troop leader wondered whether providing an incentive to whomever sold the most girlscout cookies would

have an effect on the number cookies sold. She provided a big incentive to one troop (trip to Hawaii), a lesser

incentive to a second troop (bicycle), and no incentive to a third group, and then looked to see who sold more cookies.

Troop 1(Hawaii)

65946

Troop 2(bicycle)

68542

Note: 5 girls in each troop

Troop 3(nada)

0401 0

x = 6 x = 5

x = 1

What if we want to compare 3 means?One independent variable with 3 means

A girl scout troop leader wondered whether providing an incentive to whomever sold the most girl scout cookies would



n = 5 x = 10

n = 5 x = 12

n = 5 x = 14

Troop 1(nada)

108

127

13

Troop 2(bicycle)

1214101113

Troop 3(Hawaii)

149

191315

What is Independent

Variable?

How many groups?

What is Dependent Variable?

How many levels of the Independent

Variable?

Main effect of incentive: Will offering an incentive result in more girl scout cookies being sold?

If we have a “effect” of incentive then the means are significantly different from each other• we reject the null• we have a significant F• p < 0.05

We don’t know which means are different from which …. just that they are not all the same

To get an effect we want:• Large “F”

- big effect and small variability• Small “p”

- less than 0.05 (whatever our alpha is)

Hypothesis testing:

Step 1: Identify the research problem

Describe the null and alternative hypotheses

Is there a significant difference in the number of cookie boxes sold between the girlscout troops that were

given the different levels of incentive?

Hypothesis testing:

Decision rule

= .05

Critical F (2,12) = 3.98

Degrees of freedom (between) = number of groups - 1

Degrees of freedom (within) = # of scores - # of groups

= 3 - 1 = 2

= (15-3) = 12*

*or = (5-1) + (5-1) + (5-1) = 12.

α= .05

Critical F(2,12)

= 3.89

F (2,12)AppendixB.4 (pg.518)

ANOVA table

?

df MS F

? ?

?

Source

Between

WithinTotal

??

SS

?

?

?

“SS” = “Sum of Squares”- will be given for exams

- you can think of this as the numerator in a standard

deviation formula

?

?

?

ANOVA table

128

df MS F

# groups - 1

# scores - number of groups

# scores - 1

2

12

14

Source

Between

WithinTotal

88

40

SS

? ?

????

“SS” = “Sum of Squares”- will be given for exams

3-1=2

15-3=12

15- 1=14

ANOVA table

ANOVA table

128

df MS F

2

12

14

Source

Between

WithinTotal

88

40

SS

MSbetween

MSwithin

SSwithin

dfwithin

20

7.33

SSbetween

dfbetween

8812

=7.33

40 2

=20

207.33

=2.73 2.73

402

8812

? ?

?

Make decision whether or not to reject null hypothesis

2.73 is not farther out on the curve than 3.89 so, we do not reject the null hypothesis

Observed F = 2.73Critical F(2,12) = 3.89

Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold

F(2,12) = 2.73; n.s.

The average number of cookies sold for three different incentives were compared. The mean number of cookie boxes sold for the“Hawaii” incentive was 14 , the mean number of cookies boxes sold for the “Bicycle” incentive was 12, and the mean number of cookies sold for the “No” incentive was 10. An ANOVA was conducted and there appears to be no significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 12) = 2.73; n.s.

Let’s do same problemUsing MS Excel

A girlscout troop leader wondered whether providing an incentive to whomever sold the most girlscout cookies would



Troop 1(Nada)

108

127

13

Troop 2(bicycle)

1214101113

Troop 3(Hawaii)

149

191315

n = 5 x = 10

n = 5 x = 12

n = 5 x = 14

Let’s do oneReplication of study

(new data)

SSwithin

dfwithin

SSbetween

dfbetween

8812

=7.33

40 2

=20

207.33

=2.73

402

8812

MSbetween

MSwithin

# groups - 1

# scores - number of groups

# scores - 1

3-1=2

15-3=12

15- 1=14

F critical

(is observed F greater than critical F?)

P-value

(is it less than .05?)

No, so it is not significantDo not reject null

No, so it is not significantDo not reject null




Also p-value is not smaller than 0.05 so we do not reject the null hypothesis

Step 6: Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold




Conclusion: There appears to be no effect of type of incentive on number of girl scout cookies sold

F(2,12) = 2.73; n.s.

The average number of cookies sold for three different incentives were compared. The mean number of cookie boxes sold for the“Hawaii” incentive was 14 , the mean number of cookies boxes sold for the “Bicycle” incentive was 12, and the mean number of cookies sold for the “No” incentive was 10. An ANOVA was conducted and there appears to be no significant difference in the number of cookies sold as a result of the different levels of incentive F(2, 12) = 2.73; n.s.

One way analysis of varianceVariance is divided

Total variability

Withingroup

variability(error variance)

Betweengroup

variability(only one factor)

Remember, 1 factor = 1 independent variable(this will be our numerator – like difference between

means)

Remember, error variance = random error

(this will be our denominator

– like within group variability

Remember, one-way = one IV

Five steps to hypothesis testing

Step 1: Identify the research problem (hypothesis)

Describe the null and alternative hypotheses

Step 2: Decision rule

• Alpha level? (α = .05 or .01)?

Step 3: Calculations

Step 4: Make decision whether or not to reject null hypothesisIf observed t (or F) is bigger then critical t (or F) then reject null

Step 5: Conclusion - tie findings back in to research problem

• Critical statistic (e.g. z or t or F or r) value?

MSWithin

MSBetweenF =

Still, difference between means

Still, variabilityof curve(s)

.Difference

between meansDifference

between meansDifference

between means

Variabilityof curve(s)Variabilityof curve(s)Variabilityof curve(s)

“Between Groups”Variability

“Within Groups”Variability

Sum of squares (SS): The sum of squared deviations of some set of scores about their mean

Mean squares (MS): The sum of squares divided by its degrees of freedom

Note: MStotal = MSwithin + MSbetween

Mean square within groups:sum of squares within groups divided by its degrees of freedom

Mean square between groups:sum of squares between groups divided by its degrees of freedom

Mean square total: sum of squares totaldivided by its degrees of freedom

MSWithin

MSBetweenF =

ANOVA

Variability within groups

Variability between groupsF =

Variability Between Groups

Variability Within Groups Variability Within Groups

“Between” variability bigger than “within” variability so

should get a big (significant) F



“Between” variability getting smaller “within” variability

staying same so, should get a smaller F

Variability Between Groups “Between” variability getting very small “within” variability staying same so, should get a

very small F


ANOVAVariability within groups


“Between” variability bigger than “within” variability so

should get a big (significant) F

“Between” variability getting smaller “within” variability

staying same so, should get a smaller F

“Between” variability getting very small “within” variability staying same so, should get a

very small F (equal to 1)

Variability Within Groups





.

Effect size is considered relativeto variability of distributions

Treatment

Effect

Treatment

Effect

x

xVariability

within groups

Variability between groups

Let’s try one

In a one-way ANOVA we have three types of variability. Which picture best depicts the random error variability (also known as the within variability)? a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above

1.

2.

3.

Let’s try one

Which figure would depict the largest F ratio a. Figure 1 b. Figure 2 c. Figure 3 d. All of the above

Variability within groups


1.

2.

3.

“F ratio” is referring to "observed F”

Let’s try one

Winnie found an observed z of .74, what should she conclude?

(Hint: notice that .74 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given

small observed z score

xsmall observed z score

x

If your observed z is within one standard deviation of the mean,

you will never reject the null

Let’s try one

Winnie found an observed t of .04, what should she conclude?

(Hint: notice that .04 is less than 1) a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given

small observed t score

x

Let’s try one

Winnie found an observed F ratio of .9, what should she conclude? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given

1.

2.

3.

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