BioStats Exam 1

population

the entire group of objects in our study

parameters

measurements on populations

sample

represents part of a population

statistics

measurements on samples

(experimental) unit

an object about which we collect data or measurements

person, thing, events, etc.

variable

a property of a unit which we wish to measure

height, eye color, etc.

qualitative and quantitative

types of variables

qualitative variable (categorical)

classifies the units into categories, which may or may not have a natural ordering to them

no math possible

quantitative variable

has numerical values that are measurements (height, weight, etc.) or counts

math can be applied to this

continuous or discrete

a quantitative variable can be…

continuous

a quantitative variable is _____ if it can take any value in an interval (has decimals)

discrete

a quantitative variable is _____ if it can take on a limited or countable number of values (whole numbers)

collect data and then make decisions

the goal of every statistical study is to…

observational study, perform an experiment, use a simulation, and administer a survey

types of sampling techniques

observational study

researcher observes and measures characteristics of interest of part of a population but doesn’t change existing conditions

perform an experiment

a treatment is applied to part of a population and responses are observed

use a simulation

the use of a mathematical model to reproduce the conditions of a situation or process

administer a survey

an investigation of one or more characteristics of a population

census

a count or measure of an entire population

sampling

a count or measure of part of a population and is more commonly used in statistical studies

simple random, stratefied, cluster, and systematic

types of samples

simple random sample

one in which every sample of the same size has the same chance of being selected

stratefied sample

when it’s important for the sample to have members from each segment of the population

strata

subsets that members of the population that share a common characteristic in stratefied sample

cluster sample

used when the population falls into naturally occurring subgroups, each having similar characteristics

clusters

groups that population is divided into in cluster sample

systematic sample

each population member is assigned a number

a starting number is randomly selected, and then sample members are selected at regular intervals from the starting number

bias

a sample should be selected from a population randomly, otherwise it’s prone to…

representative sample

when sampled properly, we obtain a _____ of the population

representative sample

a subset of the population from which data are collected that accurately reflects the population

bias

the systematic favoring of certain outcomes

sample/systematic bias

systematic favoring of certain outcomes due to the methods employed to obtain the sample

non-response and response

types of sampling bias

non-response bias

a type of sampling bias where certain outcomes are favored when the individuals who choose to participate in a study differ from the individuals who choose to not participate

response bias

a type of sampling bias where certain outcomes are favored when participants do not respond truthfully

stem-and-leaf, dot plot, histogram, bar chart, pie chart, and time series graph

types of graphical representations of data (graphs)

stem-and-leaf

a diagram in which each observation is separated into two parts

stem

in a stem-and-leaf plot, ____ consists of all but the rightmost digit

leaf

in a stem-and-leaf plot, ____ is the rightmost digit

increasing order

to make a stem-and-leaf plot, sort the stems in _____ and draw a vertical line to the right of this list

key

every stem-and-leaf plot should be accompanied by a ____

dot plot

a graph where each observation is plotted as a dot at an appropriate place above the horizontal axis

stem-and-leaf plot

dot plot

classes, frequency

histogram is a graph where data has been grouped into intervals or _____ and the _____ of measurements in each class is noted

Rf = frequency / total number

relative frequency formula

qualitative data

bar chart similar to a histogram but uses…

touch, do not touch

in a histogram, the bars ___ each but, in a bar chart, the bars ____ each other

pie chart

a disk divided into wedge-shaped pie pieces proportional to the relative frequencies of the qualitative data

time series graph

a line graph of repeated measurements taken over regular time intervals

trends or patterns

time series graphs are good for identifying _____

bar graph

histogram

time series graph

pie chart

mean

the sum of the numbers divided by n

sample and population

types of mean

mean()

R function for mean

closer

when there’s a high value in a set of numbers, the mean moves ____ to the higher value

median

the middle number when numbers are arranged from smallest to largest

odd

if the amount of numbers is ____, the median is the middle number

even

if the amount of numbers is _____, the median is the average between the two middle numbers

sort() or median()

R function to help you find median

resistant

the median is ____ to outliers or extreme values

mode

the most frequently occurring value

more than one, no mode, symmetric

there can be ____ mode

if the frequency of each number is one, there is ____

the mode is not often used for quantitative data unless the data is ______

mode

between mean, median, and mode, ____ is the only measure which can be used for qualitative data

range

the difference between the largest value and the smallest value

range = maximum - minimum

range formula

max() - min()

using R to find range

standard deviation

a measure of the spread of the observations from the mean

variance

a measure of the squared spread of the observations from the mean

mean

standard deviation shares the same units as the…

positive

standard deviation (and variance) is typically ____

larger

the more spread out the numbers are about the mean, the ____ the standard deviation (or variance)

zero

if the observations are the same, the standard deviation (or variance) is equal to ___

square units

variance is measured in…

sd()

using R to compute standard deviation

put the numbers in the list then stat + calc + 1

TI calculator shortcut to find 1 variable statistics

interquartile range

measures the spread of the middle 50% of data

Q₂

the median = ___

Q₁

the median of the lower half of the data

Q₃

the median of the upper half of the data

Q₁

the 25^th percentile and separates the lower 25% of the data and upper 75%

Q₂

the 50^th percentile and separates 50% of the data

Q₃

the 75^th percentile and separates the lower 75% of data from the upper 25%

left skewed

Q₁ is further from the median than Q₃, then the data is ______

symmetric

Q₁ and Q₃ are the same distance from the median, then the data is approximately ____

right skewed

Q₃ is further from the median than Q₁, then the data is ____

IQR()

using R to find interquartile range

five-number summary

the minimum, Q₁, median, Q₃, and maximum (in this order)

fivenum()

using R to find the five-number summary

standard score(z-score)

tells us how many standard deviations the observed value is from the mean

z > 0

if ____, then x > mean

z < 0

if ____, then x < mean

z = 0

if ____, then x = mean

modified boxplots and z-score

two methods to detect probable outliers

potential outliers, solid dot

for a modified boxplot, observations that fall outside of the fences are ____ and are marked with a ____

absolute value of z > 3

if the _____, then x is a probable outlier

random variable

an uncertain number whose value depends on the random outcome of an experiment