Complete Statistical Methods in Psychology Assignment

NEED A STATISTICS METHODS IN PSYCHOLOGY EXPERT ONLY!!!!Showing your work (all steps) you took to solve each calculation problem, according to the method outlined in the ATTCHMENTSComplete the homework 5 from the worksheet below…can be hand written (and do not copy from coursehero or chegg) or can be in word documentYOU MUST DO IT THE WAY THE PROFESSOR HAS OUTLINED IN THE FORMULA SHEET BELOW…YOU CAN ONLY USE THE SYMBOLS HE HAS CHOSEN FOR THIS COURSE IN THE SHEET ATTAHCED
symbols.pdf

assignment_5.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
?
rho (pronounced row)
S
sum (sigma)
µ
populational mean (pronounced mu)
M
sample mean (pronounced x bar)
a
alpha
ß
beta
=
greater than or equal to
=
less than or equal to
s
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 (S)
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
PSYC 2317
Mark W. Tengler, M.S.
Assignment #5
Linear Regression
5.1
For the following set of data,
X
1
4
3
2
5
3
a.
b.
c.
Y
2
7
5
1
14
7
Compute the Pearson correlation. Determine if there is a relationship,
what type of relationship, and how strong or weak that relationship is, if
any relationship exists.
Find the linear regression equation for predicting Y from X (use the linear
regression equation formula #1 from class handout).
Use the regression equation that you derived (part b above) to compute the
predicted Y for each actual value of X. Compare the predicted Y scores to
the actual Y scores. Why is there a difference between the predicted Y
values and the actual Y values? How do you explain this difference?
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
s2 =
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
s=
x-M
deviation
=
s
stand. dev.
Z=
2
v? x –
mean = 0
standard deviation = ± 1.0
X = M + Zs
Area Under the Normal Curve
(? X)2
N
N
2
v? X –
X-µ
s
X = µ + Zs
-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) )
v(? x2 –
y
)(?
n
n
degree x & ? ???? ?????h??
degree x & ? ???? ??????????
r2 = estimate or % of accuracy of predictions
? xy-

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