Stats 6-8

Front 1

Correlation

Back 1

measures the strength of a certain type of relationship

Front 2

regression

Back 2

a numerical method for trying to predict the value of one measurement variable from knowing the value of another one

Front 3

Statistical relationship

Back 3

differs from deterministic relationship

Front 4

Deterministic relationship

Back 4

if we know the value of one variable, we can determine the value of the other exactly

Front 5

Statistically significant

Back 5

To determine, we ask what the chances are that a relationship that strong or stronger would have been observed in the sample if there really were nothing going on in the population

Front 6

Correlation of +1, -1, zero

Back 6

+1: perfect linear relationship
-1: perfect linear relationship; as one increases, other decreases
Zero: no linear relationship or indicates that the best straight line through the data on a scatterplot is exactly horizontal

Front 7

Positive correlation

Back 7

indicates variables increase together

Front 8

Negative correlation

Back 8

one variable increases, the other decreases

Front 9

Equation for line

Back 9

y = a +bx

Front 10

Out of 100%, there will be about ___ statistically significant relationships

Back 10

5%

Front 11

Even minor relationships can achieve statistical significance if the ___ ____ is ____

Back 11

sample size, large

Front 12

The regression equation is the ___

Back 12

line equation

Front 13

Problems that can affect correlations

Back 13

outliers, groups combined inappropriately

Front 14

_% of all data points are corrupted

Back 14

5%

Front 15

7 Reasons two variables could be related

Back 15

1) explanatory variable is the direct cause of the response variable
2) The response variable is causing a change in the explanatory variable
3) The explanatory variable is a contributing but not sole cause of the response variable
4) Confounding variables may exist
5) Both variables may resulst from a common cause
6) Both variables are changing over time
7) The association may be nothing more than coincidence

Front 16

Evidence of a possible causal connection exists when

Back 16

1) There is a reasonable explanation of cause and effect
2) The connection happens under varying conditions
3) Potential confounding variables are ruled out

Front 17

Percentage with the trait

Back 17

(number with trait/total)x100%

Front 18

Proportion with trait

Back 18

number with trait/total

Front 19

Probability of having trait

Back 19

number with trait/total

Front 20

Risk of having trait

Back 20

number with trait/total

Front 21

Odds of having the trait

Back 21

numberwith trait/number without, to 1

Front 22

Baseline risk

Back 22

risk without treatment or behavior

Front 23

Relative risk of an outcome for two categoris of an explanatory variable is

Back 23

the ratio of the risks for each category

Front 24

Increased risk

Back 24

(change in risk/baseline risk) x 100%

Front 25

Increased risk

Back 25

(relative risk - 1) x 100%

Front 26

To compute odds ratio

Back 26

Compute odds of a, odds for b, then a/b

Front 27

Common ways the media misrepresent stats about risk

Back 27

Baseline risk is missing, time period of risk not identified, reported risk is not necessarily your risk

Front 28

Simpson's Paradox

Back 28

Relationship appears to go in one direction if third variable is not considered, and another direction if it is

Front 29

Selection ratio

Back 29

ratio of the proportion of success from one group compared to another

Front 30

Statistically significant

Back 30

If a relationship as strong as the one observed in the sample (or stronger) would be unlikely without a real relationship in the population

Front 31

Basic steps for hypothesis testing

Back 31

1) determine the null hypothesis and the alternative hypothesis
2) Collect the data and summarize them with a single number called a test statistic
3) Determine how unlikely the test statistic would be if the null hypothesis were true
4) Make a decision

Front 32

Null hypothesis

Back 32

there is no relationship between the two variables in the population

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Alternative hypothesis

Back 33

There is a relationship between the two variables in the population

Front 34

Sacred rule

Back 34

not acceptable to use the same data to determine and test hypotheses

Front 35

Chi-square test

Back 35

steps two to four of hypothesis testing

Front 36

P-value

Back 36

probability of observing a test statistic as extreme as the one observed or more so if the null hypothesis is really true. If p-value is .05, statistically significant

Front 37

How to compute a chi-square statistic

Back 37

Compute the extected counts, assuming null hypothesis is true. Compare the observed and excted counts. Compute the chi-square statistic.

Front 38

If chi-squre statistic is at least 3.84, the p-value is .05 or less

Back 38

Conclude that the relationship in the population is real. Relationship statistically significant, reject null hypothesis (no relationship in population), accept alternative hypothesis (there is a relationship).

Front 39

If chi-square statistic is less than 3.84, the p-value more than .05

Back 39

Isn't enough evidence to conclude that the relationship in the population is real. Relationship not statistically significant, do not reject null hypothesis (no relationship in population), relationship in sample could have occured by chance

Front 40

Expected count =

Back 40

(row total)(column total)/(table total)

Front 41

Statistically significant doesn't always mean

Back 41

the two variables have a relationship

Front 42

Relative-frequency interpretation

Back 42

Simply the relative frequency, over the long run, with which the coin lands heads up

Front 43

Probability

Back 43

the proportion of time it occurs over the long run

Front 44

Determining probability of an outcome, two methods

Back 44

1) make an assumption about the physical world (know how coins are made)
2) observe relative frequenct over many, many repetitions of the situtions (flip the coin)

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Personal probability

Back 45

the degree to which a given individual beliefs the event will happen

Front 46

Probability rules

Back 46

1) If there are only two possible outcomes in an uncertain situation, then their probabilites must add to 1
2) If two outcomes cannot happen simultaneously, they are said to be mutually exclusive; the probability of one or the other of two mutually exclusive outcomes happening is the sum of their individual probabilities
3) If two events don't influence each other (independent), then the probability that they both happen is foud by multiplying their individual probabilities
4) If probability b is a subset of probability a, then b can't be higher than a's probability

Front 47

Expected value

Back 47

represents average value of any measurement over the long run, expected

Front 48

Computing expected value

Back 48

multiply possible mounts with their associated probabilities, then add them all together