Cheat sheet(math) PDF

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Summary

This document includes a cheat sheet that can help you to booster your grade for midterm&final in PSY 371 class by Dr. Ben-zeev....

Description

Statistics

Population formula

Sample formula

Population notation

Sample notation

Frequency

-

-

f

f

Cumulative frequency

-

-

cf

cf

N= ∑f

n= ∑f

N

n

Population/Sample size

Usage

Example

To represent the # of the events occurred To define a running total of frequency

Raw data: 1,1,1,2,2,2,2,2

To represent the # of participants of scores

f 1 =3 f 2=5 f 1 =3 f 2=5

cf 1=3 cf 2=5

N = ∑f = 8

Mean

Weighted mean

∑x μ= N

∑ x 1 +…+ ∑ x n N 1 +…+N n

∑x x = n

∑ x 1 +…+ ∑ x n N 1 +…+ N n

μ

x wg

x or M

x wg

To find the balance point for the distribution or the central tendency among numeric scores from an interval or a ratio scale

To determine the overall mean between two means especially when the samples are not the same size

Raw data: 3,7,4,6 Mean=

20 4

=5

x 1 =77, N=27 x 2 =64, N=42 x 3 =82, N= 15 x wg = ∑ x 1 +∑ x 2+ ∑ x3 N 1+ N 2 + N 3 =

2079 + 2688+ 1230 27 + 42 + 15 =71.39

Median

Mode

-

-

-

-

-

-

-

-

To determine the midpoint (50th percentile) of the distribution and makes the scores are divided into two equal-sized groups. It is useful to detect central tendency when there is extreme scores (Skewed distribution) To determine the most frequent score. It is useful to detect central tendency in nominal data since it is not calculated value.

Raw data, 1,2,4,5,7 Median =4 (3 ways to compute median; L&L4)

Raw data: 1,1,1,2,2,3,4,4,4,5,5,5,5 Mode=5

(x−μ)

Deviation score

Standard deviation

√

(x−x )

2

∑(x−μ) N

2

Variance

∑ (x−μ) N

√

-

-

To measure the distance between the mean and the score

sx

To measure the variability by computing the average distance between the mean and each scores

2

∑(x−x ) n−1

σx

2

∑ (x−μ) N

σ x2

s2

To measure the variability based on squared distances

Population A:11,12,13,14,15,16,17

μ=14 ( x−μ ) :-3,-2,1,0,+1,+2, +3 Raw data: 11,12,13,14,15 ( μ =13) (x−μ) = -2, -1, 0, +1, +2 σx =

√ √

4 +1+ 0 +1+ 4 5 10 = √2 = = 5 1.41

σ x2 = 2 μ =60, σ x =10 Standard deviation unit (Standardized score)

x−μ σx

x−μ sx

z

z

To identify the exact location of each score in a distribution and to compare two scores that are from different normal distributions

If x=90,

zx =

90−60 =+ 10 3.0

Pearson r (coefficients of correlation) Regression

∑ zx zy Np

∑ zx zy Np

r

r

To know how strong the relationship (strength/magnitude) is between the two variables. (-1≤r≤1)

y p = μy +β(x- μx )

y p = x y +β(x- x x )

-

-

To know the accuracy of prediction...