Expert answer:Take Statistical Methods in Psychology Midterm

Solved by verified expert:Login and complete midterm…will provide login details…really need an A on this assignmentMUST USE SCRACTH PAPER AND UPLOAD PICTURE OF WORK ONCE COMPLETE WITH THE TEST FOR THE PROFESSORSEND IT HERE AND I WILL SEND TO THE PROFESSORMUST ONLY USE THE FORMULAS AND SYMBOLS FROM THE ATTACHED WORKSHHET FROM THE COURSETEST IS TIMES FOR TWO HOURS
symbols.pdf

formula_sheet.pdf

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X, Y
variables
n
number of people in a research group or sample
N
number of people in target population
ρ
rho (pronounced row)
Σ
sum (sigma)
μ
populational mean (pronounced mu)
M
sample mean (pronounced x bar)
α
alpha
β
beta

greater than or equal to

less than or equal to
σ
populational standard deviation (sigma)
s
sample standard deviation (also will see the symbol, SD)
±
plus/minus
Order of Mathematical Operations
1.
Parentheses (innermost to outermost)
Exponents
2.
3.
Multiplying/dividing
4.
Summation (Σ)
5.
Adding/subtracting
Example:
3(X2-2XY)(2+7X2+X)2+2
(X-Y)(Y-X2)
What order would you do the calculations?
If x = 2 & y = 3
Descriptive Statistics Formula Sheet
Sample
Population
Characteristic
statistic
Parameter
raw scores
x, y, . . . . .
X, Y, . . . . .
mean (central tendency)
M=
μ=
range (interval/ratio data)
∑x
n
highest minus lowest value
deviation (distance from mean)
Deviation = (x − M )
Deviation = (X − μ )
average deviation (average
∑(x − M )
=0
n
∑(X − μ )
N
(∑ x)2
SS = ∑ x −
n
(∑ x)2
∑ x2 −
n = SS
s2 =
n−1
df
(∑ X)2
SS = ∑ X −
N
(∑ X)2
∑ X2 −
N
σ2 =
N
distance from mean)
sum of the squares (SS)
(computational formula)
variance ( average deviation2 or
2
standard deviation )
(computational formula)
2
standard deviation (average
deviation or distance from mean)
(computational formula)
Z scores (standard scores)
s=
Z=
∑X
N
highest minus lowest value
2
(∑ x)2
n
n−1
σ=
x−M
deviation
=
s
stand. dev.
Z=
2
√∑ x −
mean = 0
standard deviation = ± 1.0
X = M + Zs
Area Under the Normal Curve
(∑ X)2
N
N
2
√∑ X −
X−μ
σ
X = μ + Zσ
-1s to +1s = 68.3%
-2s to +2s = 95.4%
-3s to +3s = 99.7%
Using Z Score Table for Normal Distribution
(Note: see graph and table in A-23)
for percentiles (proportion or %) below X
for positive Z scores – use body column
for negative Z scores – use tail column
for proportions or percentage above X
for positive Z scores – use tail column
for negative Z scores – use body column
to discover percentage / proportion between two X values
1. Convert each X to Z score
2. Find appropriate area (body or tail) for each Z score
3. Subtract or add areas as appropriate
4. Change area to % (area × 100 = %)
Regression lines
(central tendency line for all
points; used for predictions
only) formula uses raw
scores
b = slope
a = y-intercept
y = bx + a
(plug in x
to predict y)
b=
(∑ x)(∑ y)
n
(∑
x)2
∑ x2 −
n
∑ xy −
a = My – bMx
where My is mean of y
and Mx is mean of x
SEest (measures accuracy of predictions; same properties as standard deviation)
Pearson Correlation Coefficient
(used to measure relationship;
uses Z scores)
r=
r=
(∑ x)(∑ y)
n
2
2
(∑
x)
2 −(∑ y) )
√(∑ x2 −
y
)(∑
n
n
degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟
degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑒𝑙𝑦
r2 = estimate or % of accuracy of predictions
∑ xy−

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