Statistics Final For Lyfe

Front 1

Confounded variables

Back 1

Two variables such that their effects on the response variable cannot be distinguished from each other

Front 2

P-Value

Back 2

The probability of the observed value or something more extreme under the assumption that the null hypothesis is true

Front 3

Power of a Test

Back 3

The probability of correctly detecting a true alternative hypothesis

Front 4

Individual

Back 4

The objects described by a set of data; person (animal), place, and thing. In a medical trial, the people in the study referred to as called Subjects

Front 5

Residuals

Back 5

The errors, or difference between the estimated response y hat and the actual measured response y collectively

Front 6

Level of significance

Back 6

Probability of rejecting a true null hypothesis

Front 7

Inferential

Back 7

Statistics involve methods of using information from a sample to draw conclusions regarding the population

Front 8

Descriptive

Back 8

Statistics involve methods of organizing, picturing, and summarizing the information from samples or populations

Front 9

Type 1 error

Back 9

Rejecting a true null hypothesis

Front 10

Placebo effect

Back 10

Occurs when a subject receives no treatment, but (incorrectly) believes he or she is in fact receiving treatment and responds favorably

Front 11

Type II error

Back 11

Failing to reject a false null hypothesis

Front 12

Lurking variable

Back 12

A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unkonw or not measured

Front 13

Quantitative variable

Back 13

A variable has a value or numerical measurement for which operations such as additions or averaging make sense.

Front 14

Qualitative variable

Back 14

A variable describes an individual by placing the individual into a category or group

Front 15

Simple random sample

Back 15

A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected

Front 16

Outlier

Back 16

A data value that falls outside the overall pattern of the graph

Front 17

Sample space

Back 17

The collection of all possible outcomes in an experiment

Front 18

Parameter

Back 18

A numerical measure that describes an aspect of the population

Front 19

Statistic

Back 19

A numerical measure that describes an aspect of a sample

Front 20

Correlation coefficient

Back 20

A numerical measure that assesses the strength of a linear relationship between two variables

Front 21

Standard error

Back 21

The standard deviation of a sampling distribution

Front 22

Data is skewed to the left when the mean is to the __ of the median

Back 22

left

Front 23

The probability of the sample space is __

Back 23

1

Front 24

The probability of any event is between __ and __

Back 24

1 and 0

Front 25

Given P(E) = 0.38, then P(E^c) = __

Back 25

1 - .38 = .62

Front 26

Let n(E) be the number of outcomes in an event E. Given n(E) = 21 and P(E) = 0.7, then n(E^c) = __

Back 26

9, Because P(E) = n(E)/n(E) + n(E^c)

Front 27

Given A and B are dependent than P(A (upside down U ) B) = ___

Back 27

P(A)P(B|A) or P(B)P(A|B)

Front 28

Given A and B are independent then P(A|B) = __

Back 28

P(A)

Front 29

Given A and B dependent then P (A or B) = __

Back 29

P(A) + P(B) - P(A and B) = P(A) + P(B) - P(A)(B)

Front 30

Given A and B are mutually exclusive than P(A (upside down U) B) = __

Back 30

0

Front 31

Given that A and B are mutually exclusive than P (A|B) = __

Back 31

0 = P(A (upside down U) B)/ P(B)

Front 32

In a normal distribution, the empirical rule states approximately __ of the observed data fall within one standard deviation of the mean

Back 32

68 %

Front 33

In a normal distribution, the empirical rule states approximately ___ of the observed data fall within two standard deviation of the mean

Back 33

95%

Front 34

In a normal distribution, the empirical rule states approximately ___ of the observed data fall within three standard deviation of the mean

Back 34

99.7%

Front 35

To test a normality of a data set, a ___ plot can be constructed using the theoretical quantiles of a normal distribution and the empirical quantiles of the data set. If the points lie closer to a ___, then the data come from a distribution that is approximately normal.

Back 35

normal quantile (or Q-Q), straight line

Front 36

If the data has a normal distribution with mean (mu) and standard deviation (theta) then the transformed z-score: z= x -(mu)/(theta) has a ___ with mean of __ and standard deviation

Back 36

standard normal distribution, 0, 1

Front 37

Suppose that x-distribution has a normal distribution. The sample mean follows a ___

Back 37

normal distribution

Front 38

Suppose that x-distribution has a normal distribution with mean (mu) ands standard deviation (theta). A statistic x bar - mean/ s/ square root of n follows a ___ distribution with ___ degrees of freedom

Back 38

Student's t, n -1 = sample size - 1

Front 39

If x-distribution has a normal distribution with mean (mu) and standard deviation (theta), then z^2 = (x-mean/theta)^2 follows a ___ distribution with __ degrees of freedom

Back 39

X^2, 1

Front 40

As the sample size increase, the maximal margin of error ___

Back 40

decreases

Front 41

List three basic principles of experimental design:

Back 41

Randomization, Blocking, and Replication

Front 42

What is a discrete variable?

Back 42

A variable that can only be a whole number (1,2,3,4) not like 1.5,2.37 and such

Front 43

What is a continuous variable?

Back 43

A variable where the values can be anything in between 1 or 2, 2 and 3 and so forth (values could be 2, 3.47, 6...)

Front 44

Nominal measurement

Back 44

Categorical data and numbers that are simply used as identifiers or names represent a nominal scale of measurement. Numbers on the back of a baseball jersey and your social security number are examples of nominal data. If I conduct a study and I'm including gender as a variable, I may code Female as 1 and Male as 2 or visa versa when I enter my data into the computer. Thus, I am using the numbers 1 and 2 to represent categories of data.Indicates difference.

Front 45

Ordinal measurement

Back 45

An ordinal scale of measurement represents an ordered series of relationships or rank order. Individuals competing in a contest may be fortunate to achieve first, second, or third place. first, second, and third place represent ordinal data. If Roscoe takes first and Wilbur takes second, we do not know if the competition was close; we only know that Roscoe outperformed Wilbur. Likert-type scales (such as "On a scale of 1 to 10, with one being no pain and ten being high pain, how much pain are you in today?") also represent ordinal data. Fundamentally, these scales do not represent a measurable quantity. An individual may respond 8 to this question and be in less pain than someone else who responded 5. A person may not be in exactly half as much pain if they responded 4 than if they responded 8. All we know from this data is that an individual who responds 6 is in less pain than if they responded 8 and in more pain than if they responded 4. Therefore, Likert-type scales only represent a rank ordering.
Indicates difference and direction of difference.

Front 46

Interval

Back 46

A scale that represents quantity and has equal units but for which zero represents simply an additional point of measurement is an interval scale. The Fahrenheit scale is a clear example of the interval scale of measurement. Thus, 60 degree Fahrenheit or -10 degrees Fahrenheit represent interval data. Measurement of Sea Level is another example of an interval scale. With each of these scales there are direct, measurable quantities with equality of units. In addition, zero does not represent the absolute lowest value. Rather, it is point on the scale with numbers both above and below it (for example, -10degrees Fahrenheit). Indicates difference, direction of difference, and amount of difference.

Front 47

Ratio

Back 47

The ratio scale of measurement is similar to the interval scale in that it also represents quantity and has equality of units. However, this scale also has an absolute zero (no numbers exist below zero). Very often, physical measures will represent ratio data (for example, height and weight). If one is measuring the length of a piece of wood in centimeters, there is quantity, equal units, and that measure cannot go below zero centimeters. A negative length is not possible. Indicates difference, direction of difference, amount of difference, and an absolute zero.

Front 48

What graphs are used for qualitative data?

Back 48

Pie Charts, Bar Charts

Front 49

What graphs are used for measured/quantitative/continuous data?

Back 49

XY Scatter Charts (2 variables), Line Graphs, Box plots, Stem and Leaf plots, Histograms

Front 50

Calculate the total number of combinations

Back 50

nCr or n!/r!(n-r!)

Front 51

What are some kinds of discrete distributions?

Back 51

Geometric, Binomial, Poisson

Front 52

What are some kinds of continuous distributions?

Back 52

Standard Normal, Chi Squared, Student's t

Front 53

What determines how well a binomial distribution approximates to the normal?

Back 53

However close the number events n is to 12 (rules of thumb is that the approximation works if n is greater than 5) and the probability of success p is to .5 (works best the farther away the probability of success is from 0 or 1)

Front 54

What is true about a normal distribution?

Back 54

the mean (mu) equals 0, the standard deviation equals 1, it's unimodal (has one mode), is bell shaped (mound)

Front 55

What is true about a t-distribution?

Back 55

it is symmetric about 0, it has heavier tails than a normal distribution (thus it is more prone to producing values that lie far from the mean), As it's degrees of freedom increase, it gets closer to N(0,1) (the normal distribution), Unimodal

Front 56

How do you calculate a critical value for a chi squared distribution?

Back 56

a = level of significance / 2

Front 57

What is interpolation and extrapolation within the context of linear regression?

Back 57

Interpolation is using x values that are between known x values to predict y hat.

Extrapolation is using x values that are beyond known x values to find p hat.

Example points: (0,1)(2,7)(5,13)

using an x of 4 to predict y is interpolation because it is between 0 to 5.

using an x of 7 is extrapolation because it is beyond 0 to 5.

Front 58

Calculate class width

Back 58

Max - Min data/ number of classes

Front 59

Calculate class midpoint

Back 59

Max value in class + Min value in class/2

Front 60

Calculate class boundaries

Back 60

-.5 to min value in class, +.5 to max value in class

Front 61

Calculate relative frequency

Back 61

Class frequency / Total Frequency

Front 62

Calculate a five number summary for data

Back 62

Min = lowest number in data set

Q2 = median

Q1 = median of the lower half

Q3 = median of the upper half

Max = Largest data value

Also, IQR (Interquartile range) is Q3 - Q1

Front 63

What is the formula for E in a test where mu is unknown? What is it's derivative for n?

Back 63

E = Z(critical value) x standard deviation/ square root of n

n = (z(critical) x standard deviation/ E)^2

Front 64

What is the formula for E in a test for proportion (p and q)? How about from n =

Back 64

E = z (critcial) x the square root of pq/n

n = pq x (z(critical) / E)^2

if there is no pq given, use 1/4

PS: FUCK ALL PROBLEMS THAT HAVE E

Front 65

Calculate a point estimate (the shit they use in confidence interval stuff) for proportion

Back 65

p hat = r/n

Front 66

Find the maximal margin of error for a test of proportion

Back 66

E = z(critical value) x square root of p hat x q hat/n

Front 67

Calculate a confidence interval for everything

Back 67

point estimate - E < whatever < point estimate + E

Front 68

What do confidence intervals like 95% give you?

Back 68

Critical values from z just by reading the chart (1.96)

For t though, you have to go down the left side for the closest degree of freedom and then across to the coinciding confidence interval. That gives you the critical for t.

For Chi-Squared, you use the degree of freedom to go down the line, and then go over to the number than is the compliment of the level of significance (5% level, go to .95)

Front 69

Find a point estimate when mu is unknown and/or standard deviation is unknown for two sample means.

Back 69

x bar 1 - x bar 2 = that point estimate

Front 70

What is the formula for E in a test where both mu and standard deviation are unknown for two sample sizes n?

Back 70

E = t (critical value) x square root of s1^2/n1 +s2^2/n2

Front 71

Calculate a point estimate when mu and standard deviation are unknown

Back 71

Its x bar nigga (sample mean), they give it to you.

Front 72

Calculate a point estimate when mu is unknown

Back 72

It's x bar nigga (sample mean), they give it to you

Front 73

What is the maximal margin of error when mu is unknown for two sample means?

Back 73

E = z(critical) x square root of standard deviation1^2/n1 + standard deviation2^2/n2

Front 74

What is the formula for a test statistic where mu is unknown?

Back 74

z = x bar - mu (stated in H0)/ standard deviation x square root of n

Front 75

What is the formula for a test statistic when mu and standard deviation are unknown?

Back 75

t = x bar - mu (stated in H0)/s/ square root of n

Front 76

What is the formula for a test statistic of proportion?

Back 76

z = p hat - p / square root of pq/n

Front 77

For linear regression, the degree of freedom is

Back 77

n - 2

Front 78

What is the formula/formulas for a binomial distribution?

Back 78

P(r) = nCrp^rq^n-r

mean (mu) = np

standard deviation = the square root of npq

when approximating to the normal use

z = x - mu / standard deviation

Front 79

What is the formula/formulas for a geometric distribution?

Back 79

P(n) = pq^n-1

mean (mu) = 1/p

standard deviation = (square root of q) / p

Front 80

What is the formula/formulas for a poisson distribution?

Back 80

P(r) = e^-theta x theta / r!

mean (mu) = theta

standard deviation = the square root of theta

For approximating to the binomial use

theta = np

Front 81

What are the formulas for degree of freedom for Chi-Squared based tests?

Back 81

(C-1)(R-1)

C = Number of columns

R = Number of Rows

or

k -1 = df

k = number of categories

(depends on the situation)

Front 82

When do we reject H0 (null hypothesis)

Back 82

When a > P-Value

Front 83

What is the test statistic for two proportions? how do you calculate p bar?

Back 83

p hat 1 - p hat 2 / p bar x q bar/n1 + p bar x q bar/n2

p bar = total r / total n