Statistics Vocabulary

Front 1

Margin Of Error Of A Sample Proportion

Back 1

The margin of error is the half-width of a confidence interbal. The confidence interval for a proportion is: p ̂±z^* √((p ̂(1-p ̂ ))/n)

Front 2

Margin Of Error Of A Sample Mean

Back 2

The half-width of a confidence interval for a sample mean. x ̅±t^* s/√n

Front 3

Binomial Distribution Formula

Back 3

P(x=k)=(n/k) p^k (1-p)^(n-k)

Front 4

Binomial Distribution Expected Value

Back 4

Expected Value = sample size x proportion. EV=np

Front 5

Binomial Distribution Standard Deviation

Back 5

σ_x=√(np(1-p))

Front 6

Technical Conditions For A 1-prop Ztest OR Interval

Back 6

.The data must be a simple random sample from the population of interest.
.nπ_0≥10 and n(1-π_0)≥10

Front 7

Technical Conditions for A T-test OR Interval

Back 7

.The data must be a simple random sample from the population of interest.
.The sample size must be greater than or equal to 30 or it must be normally distributed.

Front 8

Technical Conditions For A 2-prop Ztest OR Interval

Back 8

.Test:
-The data must be randomly assigned to treatment groups or a simple random sample from the population of interest.
-n_1 (p_c ) ̂≥5 AND n_1 (1-(p_c ) ̂)≥5
-n_2 (p_c ) ̂≥5 AND n_2 (1-(p_c ) ̂)≥5
-p ̂_c=(p ̂_1+p ̂_2)/(n_1+n_2 )

.Interval:
-The data must be randomly assigned to treatment groups or a simple random sample from the population of interest.
-There must be 5 successes and 5 failures in each group.

Front 9

Technical Conditions For A 2-sample T-test OR Interval

Back 9

.The data must be randomly assigned to treatment groups or a simple random sample from the population of interest.
.Both sample sizes must be greater than or equal to 30 or normally distributed.

Front 10

Technical Conditions For The Difference Between Two Means (paired) T-test

Back 10

The technical conditions are the same as a 1-sample t-procedure but the observational units are the pairs and the data are the differences between the two groups.
.The data must be a simple random sample from the population of interest.
.The sample size must be greater than or equal to 30 or it must be normally distributed.

Front 11

Technical Conditions For A x^2 GOF Test

Back 11

.The data must be a simple random sample from the population of interest
.The expected counts in each box must be 5.
.df=(r-1)(c-1)

Front 12

Technical Conditions For A x^2 Test Of Independence

Back 12

.The observations are a simple random sample from the population of interest.
.The expected counts are at least 5 in each category.
.df=(r-1)(c-1)

Front 13

Technical Conditions For A x^2 Test Of Equal Proportions Or Homogeneity

Back 13

.The data must be randomly assigned to treatment groups or be a simple random sample from the population of interest.
.The expected counts are at least 5 in each category.

Front 14

Technical Conditions For The Slope Of A Regression Line OR Interval

Back 14

.The data must be a simple random sample from the population or interest or be randomly assigned to treatment groups.
.The 2 variables must be linearly related.
.For any x-value the y-values must be evenly distributed across the x-axis.
.The standard deviation of the residuals are evenly distributed b±t^* SE(b)
.df=n-2

Front 15

Technical Conditions For A Correlation Coefficient Test

Back 15

.The data must be a simple random sample from the population of interest.
.Both variables must be normally distributed t= (r√(n-2))/√(1-r^2 )

Front 16

Expected Value Formula And Definition

Back 16

Multiply each outcome by its probability and then add these values over all possible outcomes.
E(x)=∑x_i (p(x_i ) )

Front 17

Regression Equation And Meaning

Back 17

The line that achieves the exact minimum value of the sum of squared residuals.
ŷ=a+bx

Front 18

Formula And Meaning Of Slope

Back 18

Predicted change in response (y) variable associated with a 1 unit increase in explanatory variable.
b=r(s_y/s_x)

Front 19

Formula And Meaning Of y Intercept

Back 19

When the explanatory (x) variable is 0 this is where the response (y) variable would be.
a=y̅-bx̅

Front 20

Outlier Calculation

Back 20

x>Q3+(1.5xIQR)=outlier

x<Q1-(1.5xIQR)=outlier

Front 21

CLT For The Sampling Distribution Of A Sample Proportion

Back 21

√(p(1-p)/n)

Front 22

CLT For The Sampling Distribution Of A Sample Mean

Back 22

σ_x=σ/√n

Front 23

Z-score Or Standardization

Back 23

Subtract the mean from the value of interest and divide by the standard deviation to find the z-score.

Front 24

General Meaning Of A Confidence Level

Back 24

This is a measurement of how confident you are that the interval does contain the true parameter value. In the long run after repeated sampling and construction of intervals, _% of those intervals will contain the true population parameter.

Front 25

General Meaning Of A Confidence Interval With Magnitude

Back 25

Used to estimate the true value of a population parameter.

Front 26

General Meaning Of Probability

Back 26

Proportion of times an event would occur if the random process was repeated many times.

Front 27

General Meaning Of Statistical Significance

Back 27

A sample result is said to be statistically significant if it is unlikely to occur due to random sampling variability alone.

Front 28

Forms Of Bias

Back 28

Sampling Bias:
.sampling bias
.voluntary response bias
.convenient sampling bias
.judgemental bias

Survey Bias
.response bias
.non-response bias
.wording bias
.undercoverage

Front 29

Probability Addition Rule

Back 29

Pr(E or F)=Pr(E) + Pr(F) - Pr(E and F)

Front 30

Probability Multiplication Rule

Back 30

Pr(A and B)=Pr(A) x Pr(B)

Front 31

Conditional Probability

Back 31

This is the chance that one event will occur given that the second event has already occured. Pr(A/B)=Pr(A and B)/Pr(B)

Front 32

Independence In Probability

Back 32

This is the likeliness that one event is unaffected by another.
Pr(A and B)=Pr(A)xPr(B)

Front 33

Mutually Exclusive In Probability

Back 33

Two events are mutually exclusive if it is impossible for them to occur together. Pr(A or B)=Pr(A)+Pr(B)

Front 34

Relative Risk Meaning And Interpretation

Back 34

p̂_A/p̂_B =relative risk
This is how much more effective one thing is than another. The risk you are taking with one treatment over another.

Front 35

Type 1 Error

Back 35

This is when you reject the null hypothesis when it is actually true. "False Alarm"

Front 36

Type 2 Error

Back 36

This is when you fail to reject the null hypothesis when it is actually false. "Missed Opportunity"