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Stats symbols sheet

A list of the formulas and statistics symbols needed to understand the...

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Data Analysis and Presentation (PSYC 3002)

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Walden University

Academic year: 2017/2018

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Alphabetical Statistical Symbols:

Symbol Text

Equivalent

Meaning Formula Link to Glossary

(if appropriate)

a Y- intercept of least square regression line

a =y− xb , for line y = a + bx Regression: y on x

b Slope of least squares regression line

b =

∑ −

∑ − −

( )

( )( )

x x

x x y y for line y = a + bx

Regression: y on x

B (n, p) Binomial distribution with parameters n and p

Discrete probability distribution for the probability of number of successes in n independent random trials under the identical conditions.

If X follows B (n, p) then, P (X = r) = r r rn

C p (, 1 −p)−

Where, 0 < p <1, r = 0,1,2, ..

Binomial Distribution

c Confidence level c=P(−zc<Normal )1,0( <zc) Confidence interval

Cr

n n-c-r Combinations (number of combinations of n objects taken r at a time)

(! )!

!

r n r

Cr

n −

= , where n ≥ r

C,rn n-c-r Combinations

(number of combinations of n objects taken r at a time)

(! )!

!

, r n r

C rn = − , where n ≥ r

Cov (X, Y) Covariance between X and Y

Covariance between X & Y

Cov (X) =E [(X-E (X))(Y- E (Y)]

CV Coefficient of variation CV= Arithmaticmean

StandardDeviation .

df Degree(s) of freedom

Equivalent

(if appropriate)

E Maximal error tolerance E zc n

σ = for large samples.

E (f (x)) Expected value of f (x)

E (f (x)) = ∑f x)( P x)(

f Frequency f = number of times score. F F-distribution variable F=

2 2

2 1

where n 1 and n 2 are the

corresponding degrees of freedom.

F-distribution, Hypothesis testing for equality of 2 variances.

F (x) or Fx Distribution function ∫ ∞−

=

Fx fxdx

f (x) or fx Probability mass function

Depends on the distribution. fx≥ 0 & ∫ x

fxdx = 1.

H 0 H-naught Null hypothesis. The null hypothesis is the hypothesis about the population parameter.

Testing of hypothesis

H 1 H-one Alternate hypothesis. An alternate hypothesis is constructed in such a way that it is the one to be accepted when the null hypothesis must be rejected.

Testing of hypothesis

IQR Interquartile range IQR = Q

3 - Q 1

Measures of central tendency. MS M-S Mean square MS=

df

SS

Analysis of variance (ANOVA)

n Sample size. n = number of units in a sample. N Population size N = Number of units in the population.

Equivalent

(if appropriate)

R Sample Correlation coefficient [ ( [*)] ( )]

var ( ), SDX SDY

Co ianceX Y r=

r

2 r-square Coefficient of determination

( )

2 2 r =Correlationcoefficient

R 2 r-square Multiple correlation coefficient 2

21

meansquareerror R = −

S Sample standard deviation 1

( ) 2

−

= ∑

x x s for ungrouped data.

() 1

( ) 2

−

=

∑

f x x s for grouped data.

Measures of dispersion

2

s

S-square Sample variance 1

2 ( ) 2

−

=

∑

x x

s for ungrouped data.

() 1

2 ( ) 2

−

=

∑

f x x

s for grouped data

Measures of dispersion

2 Se s-e- square Error variance n

sumofsquaresofresiduals Se 2 =.

SD Sample standard deviation 1

( ) 2

−

=

∑

x x s for ungrouped data.

() 1

( ) 2

−

=

∑

f x x s for grouped data.

skb Bowley’s coefficient of skewness skb =

( )

) ( )

3 1

( 3 2 2 1

Q Q

Q Q Q Q

−

− − −

Measures of skew ness

skp Pearson’s coefficient of skewness skp =

S dard Deviation

Mean Mode

tan

−

Measures of skew ness

Equivalent

(if appropriate)

SSx Sum of Squares SSx=∑(x−x) 2 for ungrouped data.

SSx=∑f(x−x) 2 for grouped data.

t Student’s t variable.

n

Normal

t

χn 2

)1,0(

=

t-distribution

tc t critical The critical value for a confidence level c.

tc=Number such that the area under the t distribution for a given number of degrees of freedom falling between −tcand tc is equal to c.

Testing of hypothesis

Var (X) Variance of X Variance of X Var (X) = E (X- μ) 2

x Independent variable or explanatory variable in regression analysis

Eg. In the study of, yield obtained & the irrigation level, independent variable is, X= Irrigation level.

x x-bar Arithmetic mean or Average of X scores. n

x x

∑

= for ungrouped data.

∑

=

fx x for grouped data.

Measures of central tendency

y Dependent variable or response variable in regression analysis

Eg. In the study of, yield obtained & the irrigation level, dependent variable is, Y= Yield obtained. Z Z-score Standard normal variable (Normal variable with mean = 0 & SD = 1)

−μ

x z , where X follows

Normal (μ,σ).

Standard normal distribution

zc z critical The critical value for a confidence level c.

zc= Number such that the area under the standard normal curve falling between −zc and zc is equal to c.

Testing of hypothesis

Confidence interval

Symbol Text

Equivalent

Meaning Formula Link to Glossary (if

appropriate)

μ Mu Arithmetic mean or Average of the population.

N

∑x

μ=

μ= E (x) = ∑xPx)(

μr Mu-r r

th central moment

μr= E [(X- μ)

r] Measures of central tendency.

μ'r Mu-r-dash r

th Raw moment μ'r = E (Xr) Measures of central tendency. ρ Rho Population correlation coefficient

( *) ( )

var ( , )

SD X SDY

Co ianvce X Y

ρ=

∑ Sigma Summation ∑x= Sum of x scores.

σ Sigma Population Standard Deviation N

∑ x−

=

( μ) 2 σ

σ= E[(x−μ 2 ]) = ∑(x−μ) 2 Px)(

Measures of dispersion

σ

2 Sigma square Population variance

N

∑ x−

=

2 ( μ)

σ

Measures of dispersion

Mathematical Statistical Symbols:

Symbol Text

Equivalent

Meaning Formula Link to Glossary

(if appropriate)

! Factorial Product of all integers up to the given number

n! = n (n-1) (n-2) ........ 1. 0! = 1 c Complement not

For example: A

c is not A ∪ Union or For example:(A∪B) is happening of either event A or event B

Equivalent

(if appropriate)

∩ Intersection And For example: (A∩B) is happening of both event A and event B

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Stats symbols sheet

Course: Data Analysis and Presentation (PSYC 3002)

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Students shared 22 documents in this course

University: Walden University

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Alphabetical Statistical Symbols:

Symbol Text

Equivalent

Meaning Formula Link to Glossary

(if appropriate)

a Y- intercept of least

square regression line a = xby −, for line y = a + bx Regression: y on x

b Slope of least

squares regression

line

b = ∑−

∑

−−

)( 2

))((

yyxx for line y = a + bx

Regression: y on x

B (n, p) Binomial

distribution with

parameters n and

Discrete probability

distribution for the

probability of number

of successes in n

independent random

trials under the

identical conditions.

If X follows B (n, p) then,

P (X = r) = rnr

npp

−

−)1(,

Where, 0 < p <1,

r = 0,1,2, ...n

Binomial Distribution

c Confidence level ))1,0(( cc zNormalzPc <

−

Confidence interval

n n-c-r Combinations

(number of

combinations of n

objects taken r at a

time)

)!(!

rnr

−

=, where n ≥ r

Crn, n-c-r Combinations

(number of

combinations of n

objects taken r at a

time)

)!(!

,rnr

Crn −

=, where n ≥ r

Cov (X, Y) Covariance

between X and Y

Covariance between

X & Y

Cov (X) =E [(X-E (X))(Y- E (Y)]

CV Coefficient of

variation CV= meanArithmatic

DeviationdardS tan .

df Degree(s) of freedom

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Stats symbols sheet

Data Analysis and Presentation (PSYC 3002)

Walden University

Comments

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Related Studylists

Preview text

Alphabetical Statistical Symbols:

Symbol Text

Equivalent

Meaning Formula Link to Glossary

(if appropriate)

∑ −

∑ − −

( )

( )( )

x x

C p (, 1 −p)−

Cr

(! )!

!

Cr

C,rn n-c-r Combinations

(! )!

!

C rn = − , where n ≥ r

Equivalent

(if appropriate)

E (f (x)) = ∑f x)( P x)(

=

Fx fxdx

IQR Interquartile range IQR = Q

3 - Q 1

df

SS

Equivalent

(if appropriate)

r

( )

21

( ) 2

−

−

= ∑

() 1

( ) 2

−

−

=

∑

∑

2

s

2 ( ) 2

−

−

=

∑

s for ungrouped data.

() 1

2 ( ) 2

−

−

=

∑

∑

s for grouped data

( ) 2

−

−

=

∑

() 1

( ) 2

−

−

=

∑

∑