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X = μ = 0 Finish later X Population variance = the mean squared deviation Deviation is distance from the mean X-μ = X-μ Sum of Squares = SS = the sum of the squared deviation scores Degrees of freedom df =n-1

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I made this "cheat sheet" to help me keep my calculations and work organized rather than use a pen and paper. I also helped me to check my work. It's not pretty and I may be the only person that can read it well but generally you just plug in numbers to the grey boxes and the calculations will take care of themselves. I spent a lot of time on this so I hope somebody else can get some use out of it. Enjoy!

### Transcript of Statistics Worksheet for Statistics and Research Methods in Psychology course

X =μ =

0

Finish laterX

Population variance = the mean squared deviation

Deviation is distance from the mean

X-μ =

X-μ

Sum of Squares = SS = the sum of the squared deviation scores

Degrees of freedom df =n-1

Z-score for a sample

X f fX5 1 54 2 83 3 92 3 61 1 1

29

Cumulative frequency & %

X f cf c%0 #DIV/0!0 #DIV/0!0 #DIV/0!0 #DIV/0!0 0%

N=

∑X

∑X =

Cohen's d

Ch7

Standard error

Z-score sample means

6

Z-score -

binomial distributionp(A) = p and p(B) = q

19 Scoresμ= 30M= 31.9SS= 220.5

Step one: state the hypothesis and set alpha level t critical values

2 tails 1 tail α = .05 1.96 1.65

α = α = .01 2.58 2.33critical region = 2.042 α = .001 3.3 ?

Step two: locate the critical region

18

Step 3: calculate the test statistic

a. calculate sample variance

12.25

b. compute estimated standard error

0.8

2.37

Sample size n=

Ho = μx

H1 ≠ μx

df = n-1

calculte sample t statistic

Step 4: make a decision about H0 and state a conclusion

Measurin effect size: cohen's d

Measure % of variance

Construct confidence interval+ -

18

12.25

0.80

2.366

0.54

0.24

+ -

33.80 26.30

n= Estimated standard errorStep 1. is it 1 or 2 tailsStep 2. α =

Pooled varianceSample A Sample B

MSS t - statistic

n=n-1 -1 -1

0 0

Confidence intervalt critical values

2 tails 1 tail F-max α = .05 1.96 1.65

α = α = .01 2.58 2.33 r^2critical region = 2.447 α = .001 3.3 ?

n= 4Sum of Squares X

000000

0 0ss= 0

H0: μ1 = μ2 or μ1 - μ2 = 0H1

Step 3. dfStep 4. t critical

Cohen's d

Ho = μx

H1 ≠ μx

X2

Include T for two sample sizes

Estimated standard error

Pooled variance

t - statistic

Confidence interval + -

#DIV/0!

0

#DIV/0!

#DIV/0!

+hand

Do by hand

#DIV/0!

-hand

Hypothesis test and effect size treatment treatment Difference1 0 0

Step 1: State the hypothesis and select alpha 2 0 0H0:μD = 0 3 0 0

4 0 0Step 2: locate the critical region 5 0 0

df = M S^2

Step 3: calculate the t SSSample variance n

Use sample mean and hypothesized pop. Mean a nd standard error to compute t statt=d r^2

D2

H1:μD ≠ 0

T critical

SMD =

Magnitude of d

Evaluation of Effect Size

Percentage of Variance Explained,

r2

d = 0.2

Small effect (mean difference around 0.2 standard deviation) r2 = 0.01

Small effect

d = 0.5

Medium effect (mean difference around 0.5 standard deviation) r2 = 0.09

Medium effect

d = 0.8

Large effect (mean difference around 0.8 standard deviation) r 2 = 0.25

Large effect

T statistic

Estimated standard error

Cohen's D

Confidence interval

Sample variance

Difference score = D=X2-X1

Null hypothesis = H0:μD = 0

r2

I II III

df= 2 -3 SourceBetween

N= 0 Withinn= n= n= G= 0 TotalM= M= M= ή =T= T= T= n= HSD=SS= SS= SS= k= 3

2

-3

-1

#DIV/0!

0

#DIV/0!

#DIV/0!

0.00

#DIV/0!

#DIV/0!

H0: Make a decision about H0 and state a conclusionH1:

∑X2=

dfbetween = k-1

dfwithin =N-k

dftotal = N-1

SSwithin = ∑SSinside each treatment

SS df MS#DIV/0! 2 #DIV/0! #DIV/0!

0 -3 0.00#DIV/0! -1#DIV/0!

Make a decision about H0 and state a conclusion

F =

Analysis of varianceNotes

Sample A Sample B Sample C Sample D add probability for type 1 errorN = add how to write the findingsG =

Source SSn = Between #DIV/0!k= Within 0

T = Total #DIV/0!SS =

= -1

= 0

Critical region =

Step 3: perform the analylis

= #DIV/0!

= 0

= #DIV/0!

= -1

∑X2 =

Step 1: State the hypothesis and specify the alpha level

H0 = μ1 = μ2 = μ3

H1 = Atleast one of the treatment means is different

Step 2: Locate the critical region : Obtain values for dfbetween and dfwithin

dfbetween = k-1

dfwithin =N-k

a. Perform the analysis of SS

SSwithin = ∑SSinside each treatment

b. perform the analysis of df

dftotal = N-1

= -1

= 0

c. calculate the MS values

= #DIV/0!

= #DIV/0!

= #DIV/0!

Source SS df MSBetween 0 0 0 Within 0 0 0Total 0 0

Size effect ANOVA

= #DIV/0!

Tukey's HSD Test

= #DIV/0!

dfbetween =

dfwithin =

d. Compute the F-ratio

Make a decision about H0 and state a conclusion

F =

df MS-1 #DIV/0! #DIV/0!0 #DIV/0!

-1

F =

Factor B

0n= 12 n= 12M= M=T= T= N=

Factor aSS= SS= G=

0n= 12 n= 12M= M=T= T=SS= SS=

0 0

Stage 1

640

47

0

36 enter yourself

0

or

3 nter yourself

TROW1=

TROW2=

∑X2=

TCOL1= TCOL2=

dftotal = N-1

SSwithin = ∑SSinside each treatment

dfwithin = ∑dfeach treatment

dfbetween = number of cells - 1

0

39

Stage 2

0

0

0

1

0.00

0

0

0

#DIV/0!

SSbetween + SSwithin = SStotal

dfbetween + dfwithin = dftotal

dfA = number of rows -1

dfB = number of columns -1

SSAxB=SSbetween-SSA-SSB

dfAxB=dfbetween-dfA-dfB

#DIV/0!

#DIV/0!

Measuring effect size

0.00

0.00

0.00

48 0.000 0.00

640 0.00

Source SS df MS FBetween 0 3Factor A 0 1 0 1 36 #DIV/0!Factor B 0 1 0 1 36 #DIV/0!A x B 0 1 0 1 36 #DIV/0!Within 0 36 0.00Total 640 47

ή2 for factor A =ή2 for factor B =ή2 for factor AxB =

Factor B

0n= 8 n= 8 n= 8M= M= M=T= T= T= N=

Factor aSS= SS= SS= G=

0n= 8 n= 8 n= 8M= M= M=T= T= T=SS= SS= SS=

0 0 0

Stage 1

0ignore

47

0

42

0

or

5 nter yourself

TROW1=

TROW2=

∑X2=

TCOL1= TCOL2= TCOL3=

dftotal = N-1

SSwithin = ∑SSinside each treatment

dfwithin = ∑dfeach treatment

dfbetween = number of cells - 1

0

47

Stage 2

0

0

0

2

0.00

0

0

0

#DIV/0!

SSbetween + SSwithin = SStotal

dfbetween + dfwithin = dftotal

dfA = number of rows -1

dfB = number of columns -1

SSAxB=SSbetween-SSA-SSB

dfAxB=dfbetween-dfA-dfB

#DIV/0!

#DIV/0!

Measuring effect size

#DIV/0!

#DIV/0!

#DIV/0!

48 #DIV/0!0 #DIV/0!

#DIV/0!

Source SS df MS FBetween 0 5Factor A 0 1 0 1 42 #DIV/0!Factor B 0 2 0 2 42 #DIV/0!A x B 0 2 0 2 42 #DIV/0!Within 0 42 0.00Total 0 47

ή2 for factor A =ή2 for factor B =ή2 for factor AxB =

n= 8X Y XY Ŷ=X + Y-Ŷ

1 4 16 3 9 12 8 -5 252 12 144 11 121 132 16 -5 253 0 0 6 36 0 4 2 44 8 64 6 36 48 12 -6 365 10 100 7 49 70 14 -7 496 14 196 12 144 168 18 -6 367 10 100 10 100 100 14 -4 168 6 36 9 81 54 10 -1 19 0 0 0 0 0 4 -4 16

10 0 0 0 0 0 011 0 0 0 0 0 012 0 0 0 0 0 013 0 0 0 0 0 014 0 0 0 0 0 015 0 0 0 0 0 0

64 656 64 576 584X Y XY

8 8Sum of the products of the deviation

72

144

64

Pearson correlation

0.75

0.5625

Sample Do I really need these?

X2 Y2 (Y-Ŷ)2

X2 Y2

MX= MY=

SSX

SSY

r2=

Population

Does rsquared go here?

Partial correlation

Regression

0.5Ŷ=X + 4

4

Standard error of estimate

2.160247

predicted variability 36

Unpredicted variability28

F-Ratios!

36.00

4.67

7.71

Source SS df MS F

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

Y

Y

regression 36 1 36.00 7.71residual 28 6 4.67total 64 7

Factor B

0n= 11 n= 11 n= 11M= M= M=T= T= T= N=

Factor aSS= SS= SS= G=

0n= 11 n= 11 n= 11M= M= M=T= T= T=SS= SS= SS=

0 0 0

TROW1=

TROW2=

∑X2=

TCOL1= TCOL2= TCOL3=

66 0.000 0.00

0.00

Source SS df MS FBetweenFactor AFactor BA x BWithinTotal

ή2 for factor A =ή2 for factor B =ή2 for factor AxB =

Goodness of fitn= 120C= 3 A B C Ddf= 2 Observed frequencies 54 38 28 0

0.333333 0.333333 0.333333 0.333333Expected frequency Expected frequancies 40 40 40 40

40

Chi-square

588.6

448.6

314

25

Chi-square for independenceObserved frequencies

n= 150 A B C Dc= 3 1 26 24 22 28r= 2 2 9 11 18 12df= 2 35 35 40 40Expected frequency Percentages 23% 23% 27% 27%

Expected frequenciesA B C D

1 23.33 23.33 26.67 26.672 11.67 11.67 13.33 13.33

35 35 40 404 3 2

3.62 3.42 0.97

0.16 0.15 0.08

E0

0.33333340

10050

10050