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Study guide and note content from units 1 - 7

1

mean

values in a data set added up and divided by the number of included values

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2

median

middle value when data set is placed in ascending order

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3

standard deviation

measure that is used to quantify the amount of set data values

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4

variance

standard deviation squared

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5

quantitative

numerical values - values that can be averaged

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6

qualitative/categorical

values that are generally words, or grouped numbers - cannot “average”

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range

the difference between the highest and lowest values in a data set

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first quartile

middle value between the minimum and the median (the median of the bottom half)

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third quartile

middle value between the median and the maximum (the median of the top half)

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Interquartile range (IQR)

the difference between the first and third quartile

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outliers

extreme values that are more than 1.5xIQR from the 1st/3rd quartile

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12

resistant

resists the effects of outliers (ie: median, IQR)

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13

nonresistant

influenced by the existence of outliers (ie: mean, standard deviation, range)

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14

boxplot

displays general distribution of data

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15

dotplot

each value represented by a dot - good for specific layout

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16

histogram

displays data grouped into bins of the same width, but displaying the varying frequencies of values

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bar chart

similar to histogram, but used for categorical variables - bars don’t touch and x-axis values are not continuous

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stem-and-leaf plot

displays all but the last digit of each individual value as a stem, and last digit is the leaf - key must be included

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19

statistical inference

method used to provide ways to answer specific questions from data with some guarantee of success

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population

entire group of individuals to which the data is being generalized

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sample

part of the group that is being studied

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22

simple random sample

all samples size *n* have the same chance of being selected

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probability sample

each member of a sample has a known chance greater zero of being selected

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stratified random sample

dividing a population into groups of similar members and then choose a SRS within each smaller group to form the full sample

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multistage sample design

process of selecting *t* counties, then *x* townships, *y* blocks in the township, and *z* households

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cluster random sample

total population is divided into groups and a sample of the groups is selected

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bias

contained in a study that systematically favors certain outcomes

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voluntary response sample

sample that consists of people who choose themselves by responding to a general appeal

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nonresponse

individual chosen for the sample can’t be contacted or refuses to cooperate

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confounding variables

two variables whose effects on a response variable cannot be distinguished from each other

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convenience sample

sample made from groups that are easiest to reach

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response bias

when a responded lies about sensitive information or telescopes the timing of an event

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33

observational study

data collector visually measures variables of interest, but does not attempt to influence the responses

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statistically significant

an observed effect too large to attribute plausibly to chance

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35

experiment

The most effective way to show a relationship between two or more variables

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double-blind experiment

experiment where neither the person nor the data collector know the variable being applied to the person

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matched pairs

special case of randomized block design used when the experiment has only two treatment conditions

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blocking

grouping similar units to allow one to draw more specific, separate conclusions

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experimental units

members on which an experiment is done

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subjects

members of a group that are human beings

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treatment

condition applied to a member or group

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factor

different explanatory variables in an experiment

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level

specific value of a factor

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placebo

dummy treatment that can have effect

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45

control group

group of people receiving a sham treatment

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randomization

use of chance to divide experimental units into groups

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principles of experimental design

control - basis comparison

Randomization - fair choice of experimental units/subjects

Replication - need to ensure that results continue to tell the same story

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hidden bias

occurs when the experimenter does not treat all the subjects the exact same way

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49

Median formula

(*N* + 1 )/2

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Standardized Score (z-score)

the number of standard deviations a value is from the mean of its respective data set

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51

normal distribution

bell-shaped curve centered at the mean of a data and distributed approximately as outlined below

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types of distribution problems

raw value →formula → z-score → normalCDF →percentile

percentile → invNorm → z-score → algebra → raw value

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symmetric, normal shape

bell-shaped as outlined on other side as well

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symmetric, but not normal

mean and median are the same, mode may be different

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skewed left

values drag out to the left (smaller numbers)

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skewed right

values drag out to the right (larger numbers)

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Best descriptive statistics when distribution is symmetric

mean and standard deviation

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Best descriptive statistics when distribution is skewed

median and IQR

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statistic

value that describes a sample (ie: sample mean, sample standard deviation)

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parameter:

value that describes a population (ie: population mean, population standard deviation)

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sampling distribution

the sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population

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steps to create a sampling distribution

Take a larger number of samples from the same population

Calculate the p-hat or x-bar for each sample

Make a histogram of these values

Examine the distribution displayed in the histogram for overall pattern (shape), center, and spread

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Bias versus Unbiased

If the sample is collected randomly, the mean of your sample should approach the mean of your population -- this is considered unbiased

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variability

as you take the many samples of a sampling distribution, the bigger the sample size of each sample, the closer each sample mean will be to the population mean (bigger sample = less variability)

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Central Limit Theorem

The sampling distribution of the means from any population whatsoever (regardless of shape) will be normal provided the sample size of the individual samples is large enough (generally 30+)

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Sample means

The mean of the x-bars (sample means) is an unbiased estimator of the population mean

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Sampling distribution requirements

SRS

*n*is greater than or equal to 30 (sample size of each individual sample is*n*)

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Sample proportions

mean of the sampling distribution of p-hat is p (therefore p-hat is an unbiased estimator of p)

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Sample proportion requirements

SRS

np & n(1-p) is greater than or equal 10

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1 proportion z-test

testing a hypothesis regarding the proportion of a single population -- looking for evidence to reject Ho and statistically support Ha

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2 prop. z-test

testing a hypothesis regarding the equivalence of the proportions of two populations -- determining if the evidence shows statistically a difference of higher/lower value between the two proportions

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1 & 2 prop z-test: step 1

hypothesis; null and alternative hypothesis, and defining the parameter(s)

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1 prop. z-test: step 2

type and conditions

A) one-proportion z-test

B) conditions (1. SRS, 2. success and failures greater than or equal 10)

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2 prop z-test: step 2

type and conditions

A) two-proportion z-test

B) conditions (1. SRS, 2. success and failures greater than or equal to 5, 3. fair to believe the two populations are independent of each other)

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1 & 2 prop. z-test: step 3

calculations; z-score, p-value

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1 & 2 prop. z-test: step 4

conclusion; “based on our evidence [p-value compared to significance level], we [reject/fail to reject] the null hypothesis, so there [is/isn’t] significant evidence to support the alternative hypothesis [in context].”

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1 prop. z-interval

using sample proportion to estimate a range of values that are likely to contain the population proportion

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2 prop. z-interval

using our sample proportions to estimate a range of values that are likely to contain the difference in population proportions

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1 & 2 prop. z-interval: step 1

defining in a sentence the population value/ difference in proportions that we are hoping to estimate (ie: “estimate the true proportion”)

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1 prop. z-interval: step 2

type and conditions

A) one proportion z-interval

B) conditions (1. SRS, 2. success and failures greater than or equal to 10)

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2 prop. z-interval: step 2

type and conditions

A) one proportion z-interval

B) conditions (1. SRS, 2. success and failures greater than or equal to 5, 3. fair to believe the two populations are independent of each other)

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1 & 2 prop. z-interval: step 3

calculation; (calculator or formula)

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1 & 2 prop. z-interval: step 4

interpretation; “we are *% confident that our interval (**,*_) contains the true proportion/difference in proportions of [parameter of interest]

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Type I Error

Rejecting Ho when Ho is true

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Type II Error

Rejecting Ha when Ha is true

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Power

The probability of accurately determining Ha as true

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How can you increase power?

Increase

*n*(the best option)Increase

*a*Move Ho and Ha further apart

Decrease

*o*

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Calculator function: x → z → %

normalcdf

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Calculator function: % → z → x

invNorm

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1 sample t-test

Testing a hypothesis regarding the mean of a single population -- looking for evidence to reject Ho and statistically support Ha

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2 sample t-test

Testing a hypothesis regarding the equivalence of the means of two populations -- determining if the evidence shows statistically a difference or higher/lower value between the two means

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1/2 sample t-test: step 1

null and alternative hypothesis, define the parameter

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1 sample t-test: step 2

Types and Conditions:

A) 1-sample t-test

B) Conditions (1. SRS, 2. Normality)

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2 sample t-test: step 2

Types and conditions:

A) 2-sample t-test

B) Conditions (1. SRS’s, 2. Normality, 3. Independence b/w)

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1/2 sample t-test: step 3

Calculations:

test statistic

degree of freedom

p-value

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1/2 sample t-test: step 4

conclusion; “based on our evidence [p-value compared to significance level], we [reject/fail to reject] the null hypothesis, so there [is/isn’t] significant evidence to support the alternative hypothesis [in context].”

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1 sample t-interval

Using our sample mean to estimate a range of values that are likely to contain the population mean

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2 sample t-interval

using our sample means to estimate a range of values that are likely to contain the difference in population means

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1/2 sample t-interval: step 1

Defining the parameter we are estimating (“estimate the true mean/difference”)

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1 sample t-interval: step 2

Type and conditions:

A) 1-sample t-interval

B) Conditions (1. SRS, 2. Normality)

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