Soc2205a/b Final Review. Healey 1e 8.2, 2/3e 7.2 Problem information: = 3.3 = 3.8 s =.53 n = 117...

Soc2205a/b Final Review

Healey 1e 8.2, 2/3e 7.2

• Problem information: = 3.3 = 3.8 s = .53

n = 117

• Use the 5-step method….• Note:

– 1 sample, Interval-ratio– Sample is large n ≥ 100

• z-test

– Question asks “Is there a significant difference?”• 2-tailed test

X

Step 4: Calculations( )

1

3.8 3.3( )

.53 117 1

.5( )

.53 116

.5( )

.53 10.77

.5( )

.0492( ) 10.16

XZ obtained

s N

Z obtained

Z obtained

Z obtained

Z obtained

Z obtained

Step 5: Interpretation

• α = .05

• Zcr = ± 1.96

• Reject Ho

• Sociology majors are significantly different (Z=10.16, α = .05)

Healey 1e 8.11, 2/3e 7.11

• Problem information:Pu = .10 Ps = .14N = 527

• Use the 5-step method….• Note for Steps 1 - 3:

– 1 sample, Nominal– Sample is large n ≥ 100

• z-test

– Question asks “Are older people more likely…?”• 1-tailed test (Note: question says do a 2 tailed test also)

X

Step 4: Calculations

( )(1 )

.14 .10( )

(.10)(.90) / 527

.04( )

.09 / 527.04

( ).00017.04

( ).013

( ) 3.06

s u

u u

P PZ obtained

P P N

Z obtained

Z obtained

Z obtained

Z obtained

Z obtained


• α = .05

• Zcr = +1.65 (for 1-tailed)

• Reject Ho

• Older people are more likely to be victimized. (Z=3.06, α = .05)

Healey 1e 9.3a, 2/3e 8.3a• Problem information:

Hockey Football

= 460 = 442

s1 = 92 s2 = 57

n1 = 102 n2 = 117

• Use the 5-step method….• Note:

– 2 samples, Interval-ratio– Sample is large n ≥ 100

• z-test

– Question asks “Is there a significant difference?”• 2-tailed test

2X

2X 2X

1X

Step 4: Calculations1 2

1 2

2 2

2 2

1 1

(92) (57)

102 1 117 1

8464 3249

101 116

83.80 28.01

111.81

10.57

X X

X X

X X

X X

X X

X X

s s

N N

Step 4: Calculations (cont.)

• Z1 2( ) (460 442) 18

1.7010.57 10.57X X

X X

Step 5: Interpretation• α = .05

• Zcr = ± 1.96

• Fail to reject Ho

• Hockey players are not significantly different from football players.

• What if the question had asked “Do hockey players have a higher aptitude score…?”

• Try conducting the significance test again!


Special Regular

Ps1 = .53 Ps2 = .59

n1 = 78 n2 = 82Use the 5-step method….

• Use the 5 step method…• Note:

– 2 samples, Nominal– Sample is large n ≥100

• z-test

– Question asks “Did the new program work? (i.e. is it better”

• 1-tailed test

2X 2X

Step 4: Calculations

1 1 22

1 2

(78)(.53) (82)(.59) 41.34 48.380.56

78 82 160u

s sN P N PP

N N

1 2

1 2

78 82 160(1 ) (.56)(.44) .2464 (.4964)(.1582) .079

(78)(82) (6396)p p u u

N NP P

N N


• Z1 2( ) .53 .59 .06

0.76.079 .079p p

s sP P


• α = .05

• Zcr = - 1.65


• The new program did not work.


– Occupational Prestige Scores for 3 Groups (Urban, Suburban, Rural)

• Use the 5 step method…• Note:

– 3 samples, Interval-ratio• F-test, One-way ANOVA

– Question asks “Are there differences by place of residence (Urban, Suburban, Rural)

– dfw = N - k = 30 - 3 = 27– dfb = k - 1 = 3 - 1 = 2– Fcr = 3.35

2X 2X

Step 4: Make Computational Table

Grand Mean= (include n-sizes too)

Urban Suburban Rural

∑Xi

∑X2

Group Means


22 2 2

2 2 2

10(49.5 52) 10(59.3 52) 10(47.2 52)

10( 2.5) 10(7.3) 10( 4.8)

10(6.25) 10(53.29) 10(23.04)

62.25 532.9 230.4

825.8

k kSSB N X X

SSB

SSB

SSB

SSB

SSB


SSW = SST - SSB

SSW = 3590 – 825.8

SSW = 2764.2

2 2

284710 (30)(52)

84710 81120

3590

SST X NX

SST

SST

SST


Within estimate (MSW)

Between estimate (MSB)

F = Between estimate (MSB) / within estimate (MSW) = 412.9 / 102.38 = 4.03

2764.2102.38

27

SSW

dfw

825.8412.9

2

SSB

dfb


• α = .05

• Fcr = 3.32

• Reject Ho

• At least one of the groups (urban, suburban, rural) is significantly different.

• (F = 4.03, df = 2, 27, α = .05)

Healey 1e 11.5, 2/3e 10.5• Problem information:Salary Union Non-union TotalHigh 21 29 50Low 14 36 50Total 35 65 100

• Is there a relationship? Answer the 3 questions…• Use the 5 step method for hypothesis test.• Note: Tabular Data, Nominal x Ordinal

– Df= (rows-1 x columns-1) = 1– α=.05, X2

cr = 3.841

2X 2X

Step 4: Expected Frequencies

Top left cell:

Top right cell:

Bottom left cell:

Bottom right cell:

(50)(35) 175017.50

100 100fe

(50)(65) 325032.50

100 100fe

(50)(35) 175017.50

100 100fe

(50)(65) 325032.50

100 100fe

Step 4: Computational Table

fo fe fo–fe (fo - fe)2 (fo - fe)2/fe

21 17.50 3.50 12.25 0.70

29 32.50 -3.50 12.25 0.38

14 17.50 -3.50 12.25 0.70

36 32.50 3.50 12.25 0.38

N=100 0.00 χ 2(obt.) = 2.16

% and Strength of Association

Salary Union Non-unionHigh 60% 44.6%Low 40% 55.4%Total 100% 100%

• Max. difference: 15.4%

• Strength: Phi =

• Weak association.

2X 2X

147.100

16.22

n

Step 5: Decision and Interpretation


• There is no significant relationship between salary levels and unionization.

• Three questions:– Association? Not significant– Strength? Weak, Phi = .147– Pattern? Union members more likely

to make high salary while non-union more likely to make low salary.

Healey 1e 14.8, 2/3e 12.8Problem information: AuthoritarianismDepression Low Moderate High TotalFew 7 8 9 24Some 15 10 18 43Many 8 12 3 23Total 30 30 30 90

• Is there a relationship? Answer the 3 questions…• Note: Tabular Data, Ordinal x Ordinal, Gamma• Use the 5 step method for hypothesis test.

– α=.05, Zcr = ±1.96

2X 2X

Step 4: CalculationsNs: 7 (10+18+12+3) = 7 (43) = 301 8 (18+3) = 8 (21) = 168

15 (12+3) = 15 (15) = 22510 (3) = 30

• Total Ns = 724

Nd: 9 (15+10+8+12) = 9 (45) = 4058 (15+8) = 8 (23) = 18418 (8+12) = 18 (20) = 36010 (8) = 80

• Total Nd = 1029


There is a weak, negative relationship between parenting style and depression.

Zobt<Zcrit. Fail to reject Ho. The association is not significant (Note: Hypothesis test. Use 5 step model)

174.01753

304

1029724

1029724

ds

ds

nn

nnG

78.275.87

1753174.

174.(190

1029724174.

1 22

GN

nnGz ds

Step 5 Interpretation

• Answering the 3 questions….

• Association? Not significant• Strength? Weak, G = -.174• Pattern/Direction? Negative, parents

who are higher in authoritarianism have children with fewer depression symptoms.*– *calculate % also.

Healey 1e 15.3, 2/3e 13.3• Is there a relationship?

– Draw scattergram– Find r and r2

– Find regression line– Calculate predicted visitors

for activity = 5 and 18

• Answer the 3 questions…• Note: Interval-ratio data,

regression and correlation• Use the 5 step method for

hypothesis test…– α=.05, df=n-2, tcr = ±2.306

Problem information:

Case Activity Visitors X Y

A 10 14B 11 12C 12 10D 10 9E 15 8F 9 7G 7 10H 3 15I 10 12J 9 2

Scattergram

Y=a+bX

Make A Computational Table

Case X Y X2 Y2 XY A 10 14 B 11 12 C 12 10 D 10 9 E 15 8 F 9 7 G 7 10 H 3 15 I 10 12 J 9 2Totals ΣX ΣY ΣX2 ΣY2 ΣXY X Y

Totals of Computational Table

X = 96 Y = 99 X²= 1010 Y²= 1107 XY= 918• 9.6• 9.9

XY

Slope (b)

* 3 decimals

b = -.367

2 2

2

( )( )

( )

(10)(918) (96)(99)

(10)(1010) (96)

9180 9504

10100 9216324

8840.37

N XY X Yb

N X X

b

b

b

b

Y-intercept (a)

42.13

)6.9)(367.(9.9

a

a

XbYa

Pearson’s r

* 3 decimals

r = -.306

2 2 2 2

2 2

( )( )

[ ( ) ][ ( ) ]

(10)(918) (96)(99)

[(10)(1010) (96) ][(10)(1107) (99) ]

324

(884)(1269)

324

1121796324

1059.15.31

N XY X Yr

N X X N Y Y

r

r

r

r

r

Coefficient of Determination (r2)and Hypothesis (t) test

• Coefficient of Determination:

• r2 = (r)2 = (-.306)2 = .094

• 9.4% of variation in visitors is explained by activity level

• Hypothesis test:

• Fail to reject Ho (t obs = -.91 < tcr = ±2.306)

Predictions* for Activity Level

• For X = 5– Ŷ = a + bX = 13.42 + (-.367)(5) = 11.6 visitors

• For X = 18– Ŷ = a + bX = 13.42 + (-.367)(18) = 6.8 visitors

• *use the calculated prediction values to draw actual regression line on the scattergram

Summary

• r = -.306

• r2 = .094

• There is a weak, negative relationship between # of visitors and activity levels for seniors. As activity levels go down, # of visitors increases. The relationship is not significant. Activity levels explain 9.4% of the variation in # of visitors.

Soc2205a/b Final Review. Healey 1e 8.2, 2/3e 7.2 Problem information: = 3.3 = 3.8 s =.53 n = 117...

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Transcript of Soc2205a/b Final Review. Healey 1e 8.2, 2/3e 7.2 Problem information: = 3.3 = 3.8 s =.53 n = 117...