Statistics and Data Analysis: Key Concepts and Methods

Nominal LOM

categories w no order

- qual and simplest LOM

ex) eye color, major

Ordinal LOM

can be ranked

- qual

ex) class ranks

Interval LOM

# data w no true 0

- quan

ex) temperature

Ratio LOM

# data with a true 0

- quan and most info

ex) height, age, money

Random sampling

everyone has equal chance of being selected

stratified sampling

divide pop into groups and select from each group

ex) students from every grade level

descriptive statistics

describe/ summarize data you already have

QUALitative data

categorical responses

QUANitative data

# data

inferential statistics

uses a sample to make conclusion about a population

systematic sampling

everyone assigned number, every __kth # is picked

ex) every 10th customer

Formula: F= N/n= kth number

cluster sampling

divide pop into clusters & select 1 or more to be included

** at least 1 group left out (diff than stratified)

ex) NYC boroughs but leaving Stat Island out

histogram

bars touching

- used w quan data

ex) weight, age...70-80, 80-90, 90-100

bar graph

space between bars

- used w qual data

ex) major and eye color... green, blue, brown

Scatterplot

shows relationship between 2 variables

- shows correlation/ association; r

boxplot

shows median, quartiles, min & max, spread of data

- can help show outliers

skewed right distribution

data toward left

- mean> median

skewed left distribution

data toward right

- median> mean

mean vs median vs mode

mean: avergae (add all and divide)

median: middle value, 50th percentile, in ordered data (avrg of 2 middle ones if uneven)

mode: mode frequent value

standard deviation

big SD= data spread out

small SD= data close to mean

quartiles and IQR

q1= first quartile 25%

q2= second quartile/ median 50 %

q3= third quartile 75%

IQR= q3-q1

Probability

- probability NEVER (-)

- between 0 & 1 (not bigger than 1)

independent vs dependent events

- one event doesnt affect probability of another event

- one event changes the probability of another event

Empirical Rule

1 sd= 68 % of data

2 sd= 95% of data

3 sd= 99.7% of data

Z Score

# of sd's from the mean

+Z = above mean

-Z= below mean

Hypothesis Testing (5 steps)

Z test = po (sigma) sd. t test = 's' sd

- null (no change) and alt (claim) hypothesis

- locate z critical values (table F with alpha & 1 or 2 tails)

- draw distribution w critical values to see rejection region

- test statistic

- decision; reject or not reject

- summary of results

p- value

- compare p-val to a to decided to reject or not

- p is low h0 goes (reject)

- p is high h0 stays (dont reject)

ex) if a= .05 and p= .02.... .02<.05 .... Reject H0

if a=.05 and p= .18.... .18>.05 .... Don't Reject H0

Correlation

relationship between2 variables

correlation coefficient (r) = sample strength and direction of correlation

+ correlation = variables same direction

- correlation = variables in opposite directions

when correlation coefficient r is close to 1 or -1, what does it mean?

strong positive or negative correlation

- closer to 0 = weak/ no correlation

In Pearson's Correlation... x = ? and y = ?

x = independent

y = dependent

simple linear regression analysis

should be done is Null is rejected from Correlation Test

Formula = y= a + bx

** can find a and b in calc

coefficient of determination

aka Explained Variable

- r^2, then make a %

- tells us how much variability in y can be explained by x

coefficient of non-determination

aka Unexplained Variable

- subtract the explained variable from 100%

- tells us what is unexplained

Chi Square test of Independence

- tests if 2 variables are related or not

. Null = variables are not dependent

. Alt = variables are dependent

. degree of freedom = (rows -1)(columns -1)...table G

. always one positive c.v.

Chi Sqaure: test stat

** need to have the expected counts (observed counts given)

- Formula for E.C. = (Row total)(Column total) / entire total

. E.C. gives # it should be if variables are independent/ not related

not true flashcard

ok

chi sq = .. data

correlation/regression = …. data

• categorical - use table of counts/ freq

• numerical - pairs of #