ST 311 Chapter 2 Notes

expirement

The process of applying some treatment then observing its effects

• almost always compares 2 or more groups

  1. treatment group

  2. control group

• can also compare 2 treatments without a control group

• units- the individuals in an experiment

units or subjects

the individuals in an experiment

observational study

process of observing and measuring specific characteristics without attempting to modify the group

• tells whats happening, cannot describe a cause/effect relationship

response variable

measures outcome of study

explanatory variable

explains/influences response variable

variability

1. treatment effects

2. experimental error

   • variability among those with the same treatment

3. lurking variables

   • variables not in the explanatory and may influence the interpretation of the relationship among response and explanatory

4. cofounding variables

   • 2 variables cofounded when the effect on the response variable cannot be distinguished

experimental error

type of variability

• variability amongst those with the same treatment

cofounding variables

type of variability

• variable not in the explanatory and may influence the interpretation of the relationship among response and explanatory variables

cofounding variables

type of variability

• the effect of different variables on the response variable cant be distinguished

principles of experimental design

1. control

   • receives no treatment

2. randomization

   • reduces or eliminates bias

3. replication

   • as much repetition or subjects to reduce variability

control group

a principle of experimental design

• receives no treatment

randomization

a principle of experimental design

• reduces or eliminates bias

• different methods such as srs, stratification

replication

a principle of experimental design

• as much repetition or units possible

• reduces variability

Randomization Methods

1. Completely Randomized Designs

2. Randomized Block Design

3. Matched Pairs Design

completely randomized designs

randomization methods

• participants randomly assigned treatments

• lurking variables applied evenly

  • any significant differences can be attributed to the explanatory variable

randomized block design

randomization method

• units subdivided into blocks

• variability within blocks less than variability between blocks

• participants within blocks are randomly assigned different treatments

matched pairs design

randomization method

• special case of randomized block design

• only has 2 groups

• participants can be grouped to pairs

• within each pair participants randomly assigned different treatments

• also can be done as before/after with the same participant

placebo effect

the tendency to react to a drug/treatment that has no real function.

subject bias

subject may want to please the researcher or hope for a specific outcome

hawthorne effect

people behave different because they know theyre being watched

bias of the researcher

• subconciously behave in ways that favor their beliefs

  • reporter biases

  • assigning subjects with biases

  • may skew results in direction that they want

blinding

individuals associated with an experiment or the researcher doesn’t know the treatment that the subjects are receiving

frequency distributions

shows how many of each occurrance happens

• often separated by intervals/ranges

• can be categorical or quantitative

measure of center

a value at or near the center or middle of a data set

• often interpreted as “typical” values for a set

• common measures of center include

  1. mean

  2. median

  3. mode

  4. iqr

uppercase sigma

Σ

denotes a sum

x

individual data value

lowercase n

# of values in a sample

uppercase N

#of values in a population

x bar

x̄ sample mean

mu

μ

population mean

unimodal

data set with 1 mode

bimodal

data set with 2 modes

multimodal

data set with more than 2 modes

mode

when data is categorical what measure of center is the best?

median

when the data is quantitative but contains outliers what is the best measure of center?

mean

when data is quantitative and contains no outliers what is the best measure of center?

histogram

graph of frequency distribution

• makes it easier to interpret pattern

Contains

1. bars of equal width drawn adjacent to each other (unless there are gaps in the data)

2. horizontal scale - represents classes of quantitative data or categories

3. vertical scale that represents frequencies

dotplot

shows each value in a data set as a do above a number line

• there is no y axis

categorical data displays

pie chars, column charts, stacked charts etc. choose based on data type

misleading graphs

• vertical axis can exaggerate differences

• y axis doesnt start at 0

• skewed stretched y axis

• 3D can make categories seem bigger or smaller

• misrepresenting areas

• using wrong type of graph to represent data

• inproper scaling

• misleading or missing labels

• not displaying full data

skewness

measure of symmetry of a distribution

• values far from the peak skew a distribution in their direction

symmetric distribution

unimodal

normal distribution

bell curve

right skew

positive skew

left skew

negative skew

uniform

equal spread

no peaks

no skew

normal/symmetric/uniform distribution

mean=median=mode

right skew

mode<median<mean

left skew

mean<median<mode

range

max value - min value

• highly affected by outlier

interquartile range (IQR)

not as affected by potential outliers like range. uses q3 and q1 difference to calculate.

five number summary

min q1 median q3 max

boxplot

visual of 5 number summary

standard deviation

measure of how much the data values deviate from the mean

• never negative

• same units as the data

  • only 0 when all values are the exact same

  • larger #s have greater variation

  • increases dramatically with outliers

  sqrt(varience)