4-Step Process Confidence Intervals

1a

1b

4-Step Process Significance Tests

2a

2b

Advantage of using a StratifiedRandom Sample

3a

Stratified random samplingguarantees that each of the strata willbe represented. When strata arechosen properly, a stratified randomsample will produce better (lessvariable/more precise) informationthan an SRS of the same size.

3b

Bias

4a

The systematic favoring of certainoutcomes due to flawed sampleselection, poor question wording,under coverage, nonresponse, etc. Bias deals with the center of asampling distribution being "off"!

4b

Binomial Distribution (CalculatorUsage)

5a

5b

Binomial Distribution (conditions)

6a

6b

Can we generalize the results to thepopulation of interest?

7a

7b

Carrying out a Two-sided test from aconfidence interval

8a

8b

Chi-Square Tests df and ExpectedCounts

9a

9b

Complementary Events

10a

Two mutually exclusive events who'sunion is the sample space

Ex. Rain / Not Rain

10b

Describe the Distribution orCompare the Distributions

11a

SOCS! Shape, Outliers, Center, Spread. Only discussoutliers if there are obviously outliers present.Be sure to address SCS in context! If it says "compare" YOU MUST USE comparison phrases like "isgreater than" or "is less than" for Center &Spread.

11b

Does ____ CAUSE ____?

12a

Association is NOT Causation! An observed association, no matterhow strong, is not evidence ofcausation. Only a well-designed,controlled experiment can lead toconclusions of cause and effect.

12b

Experimental Designs

13a

CRD (Completely Randomized Design) - All experimentalunits are allocated at random among all treatments RBD (Random Block Design) - Experimented units are put intohomogeneous blocks. The random assignment of the units tothe treatment is carried out separately within each block. Matched Pairs - A form of blocking in which each subjectreceives both treatments in random order or the subjects arematched in pairs as closely as possible and one subject ineach pair receive each treatment determined at random.

13b

Experiment or Observational Study?

14a

A study is an experiment ONLY ifresearchers IMPOSE a treatment

upon the experimental units. In an observational study researchersmake no attempt to influence theresults.

14b

Explain a P- value

15a

15b

Extrapolation

16a

Using a LSRL to predict outside thedomain of the explanatory variable (Can lead to ridiculous conclusions ifthe current linear trend does notcontinue)

16b

Factors the Affect Power

17a

17b

Finding the Sample Size (for a givenmargin of error)

18a

18b

Geometric Distribution (conditions)

19a

19b

Goal of Blocking | Benefit of Blocking

20a

The goal of blocking is to creategroups of homogenous experimentalunits The benefit of blocked is thereduction of the effect of variationwithin the experimental units.

20b

Inference for Counts (Chi-SquaredTest) (Conditions)

21a

21b

Inference for Means (conditions)

22a

22b

Inference for Proportions(conditions)

23a

23b

Inference for Regression (conditions)

24a

24b

Interpret a Residual Plot

25a

1. Is there a curved patter? If so, a linear

model may not be appropriate.

2. Are the residuals small in size? if so,

predictions using the linear model will be

fairly precise.

3. Is there increase or decreasing

spread? If so, predictions for larger

(smaller) value of x will be more variable.25b

Interpreting a Confidence Interval(Not a confidence level)

26a

26b

Interpreting a Confidence Level (themeaning of 95% confident)

27a

27b

Interpreting Expected Value/ Mean

28a

The mean/expected value of arandom variable is the long runaverage outcome of a randomphenomenon carried out a very largenumber of times.

28b

Interpreting Probability

29a

The Probability of any outcome of arandom phenomenon is theproportion of times the outcomewould occur in a very long series ofrepetitions. Probability is a long termrelative frequency.

29b

Interpret LSRL "s"

30a

s = _____ is the standard deviation ofthe residuals It Measures the typical distancebetween the actual y-values(context) and their predicted y-values (context)

30b

Interpret LSRL "SE-b"

31a

SE-b measures the standard deviation of

the estimated slope for predicting the y

variable (context) from the x variable

(context).

SE-b measures how far the estimated

slope will be from the true slope, on

average31b

Interpret LSRL Slop "b"

32a

For every one unit change in the inthe x variable (context) the y variable(context) is predicted toincrease/decrease by ____ units(context)

32b

Interpret LSRL "y"

33a

ŷ is the "estimated" value or"predicted" y- value (context) for a

given x-value (context)

33b

Interpret LSRL y-intercept "a"

34a

When the x variable (context) is zero,the y variable (context) estimated to

be `put value here`

34b

interpret r

35a

Correlation measures the strength and direction

of the linear relationship between x and y

- r is always between -1 and 1

- close to zero = very weak

-close to 1 or -1 = stronger

-Exactly 1 or -1 = perfectly straight line

-positive r = positive correlation

-negative r = negative correlation35b

interpret r ^ 2 (r squared)

36a

___% of the variation in y (context) is accountedfor by the LSRL of y (context) on x (context) or __$ of the variation in y (context) is accountedfor by using the linear regression model with X(context) as the explanatory variable

36b

Interpret Standard Deviation

37a

Standard Deviation measures spreadby giving the " typical" or "average"distance that the observations(context) are away from their(context) mean

37b

Interpret Z-Score

38a

z = value - mean / standard deviation A z-score describes how many standarddeviations a value or statistic (x, x̄,p̂, etc.) fallsaway from the mean of the distribution and inwhat direction. The further the z-score is awayfrom zero the more "surprising" the value ofthe statistic is.

38b

Linear Transformation

39a

Adding "a" to every member of a data set adds "a"

to the measures of a position, but does not

change the measures of spread or shape

Multiplying every member of data set by "b"

multiplies the measures of position by "b" and

multiplies most measures of spread by |b| but

does not change the shape

39b

Mean & Standard Deviation of aBinomial Random Variable

40a

40b

Mean & Standard Deviation of aDifference of Two Random Variables

41a

41b

Mean & Standard Deviation of aDiscrete Random Variable

42a

42b

Mean & Standard Deviation of a Sumof a Two Random Variables

43a

43b

Outlier Rule

44a

Upper Bound = Q3 + 1.5(IQR) Lower Bound = Q1 - 1.5(IQR)

IQR = Q3 - Q1

44b

Paired t-test Phrasing Hints, H0 andHa Conclusion

45a

45b

P(at least one)

46a

P(at least one) = 1 - P(none)

Ex. P(at least one 6 in three rolls) =_____

P(Get at lest one six) = 1 - P(No Sixes)

46b

The Sampling distribution of thesample mean (central limit theorem)

47a

47b

Sampling Techniques

48a

SRS - Number the entire population, draw numbers from a hat ( every setof n individuals has equal chance of selection) Stratified - Split the population into homogeneous groups, selection anSRS from each group. Cluster - Split the population into heterogeneous groups called clusters,and randomly select whole clusters for the sample. Ex. choosing a cartonof eggs actually chooses a cluster (group) of 12 eggs Census - An attempt to reach the entire population Convenience - Selects individuals easiest to reach Voluntary Response - People choose themselves by responding to ageneral appeal

48b

SOCS

49a

SHAPE: skewed left (Mean < Median) skewed right (Mean > Median) Fairly Symmetrical ( Mean = Median) Outliers: Discuss them if there are obvious ones Center: Mean or Median Spread: Range, IQR, or Standard Deviation Note ~ Also be on the lookout for gaps, clusters, or other unusual features of theddata set.

49b

SRS

50a

A simple random sample is a sampletaken in such a way that everypossible set of n individuals has anequal chance of selection.

50b

Two Events are independent if...

51a

P(B) = P(B|A^c) P(B) = P( B | A ) The knowledge of one event doestnot change the probability of theother event occurring

51b

Two Sample t-test Phrasing Hints, H0and Ha, Conclusion

52a

52b

Type I error, Type II Error, & Power

53a

53b

Types of Chi-Square Tests

54a

Goodness of Fit - use to test the distribution of one group orsample as compared to a hypothesized distribution Homogeneity: Use when you have a sample from 2 or moreindependent populations of 2 or more groups in anexperiment. Each individual must be classified based upon asingle categorical variable. Association/Independence: Use when you have a singlesample from a single population. Individuals in the sample areclassified by two categorical variables

54b

Unbiased Estimator

55a

55b

Using NormalCDF and InvNorm (Tibrand calculator tips)

56a

Normal CDF (min, max, mean,standard deviation)

InvNorm (area to the left as a

decimal, mean, standard deviation)

56b

What is an outlier?

57a

When given 1 variable data: An outlier is any value that falls morethan 1.5(IQR) above Q3 or below Q1. Regression Outlier: Any value that falls outside thepattern of the rest of the data.

57b

What is a residual?

58a

Residual = y - ŷ

A residual measures the difference

between the actual (observed) y - value

in a scatterplot and the y-value that is

predicted by the LSRL using its

corresponding x value.

In the calculator: L3 = L2 - Y1 (L1)58b

Why large Samples give moretrustworthy Results...(When collected

appropriately)

59a

59b

Why use a control group?

60a

A control group gives theresearchers a comparison group tobe used to evaluate the effectivenessof the treatment(s). (context) (gauge

the effect of the treatment comparedto no treatment at all)

60b