stats test: Exam 2: Scatterplots, Correlation, Regression, Experimental Design

Mon Nov. 10

scatterplot

relationship between two quantative variables, one on x and other on y axis

correlation coeff represents what?

r

what is r?

r is the strength of a linear relationship between two variables

ranges from -1 to 1

the abs value of the r is how strong it is

the negative/positive sign is which direction the linear relationship is going in

0 = weakest

1 = strongest

what reps coef of determination

r²

what is r²

(r² x 100) % of the variation in the response variable can be explained by its linear relationship with the explanatory variable

what is association

association is when a change in one variable changes the other variable

does association prove causation and why?

NO because association does not prove direct change in another variable - for that you need a good randomized experiment with a control group - cannot be conducted from correlation alone

association can be…

pos, neg, nonlinear (montonic - ½ of a semi circle looking graph, quadratic - semi circle), linear, no correlation, weak, strong

does an experiment prove causation?

only a well-designed experiment can prove causation

correlation

measures the strength of the linear relationship

how close data points follow a linear pattern

does not imply one change in a variable directly causes a change in the other

what is a residual in words?

the difference between the predicted value by the LSRL and the actual data point on the scatterplot

real value (y) - predicted value (y with v on top)

if a residual is positive then?

lsrl underpredicted the value

if a residual is negative then?

lsrl overpredicted value

least squares regression line (LSRL) - whats formula?

y with a v on top = b0 + b1(x)

what is b1

slope

what is b0

when x = 0, what is the y intercept

what is the least squares regression line (LSRL)? how to find on graph (manually)?

so as we said its y with v on top = b0 + b1x

its the line “best fit” for predicting the response variable from the explanatory

so to reiterate we use the explanatory variable to predict the response variable

the LSRL tries to minimize the sum of the least squared residuals

how to find slope

r multiplied by the standard deviation of y values over the standard deviation of x values

sy = stan dev of y values

sx = stan dev of x values

r(sy)/sx

as said previously what does the LSRL try to do?

the LSRL tries to minimize the sum of the least squared residuals

what is the sum of squared residuals

the vertical distance between observed y value and predicted y value

what key info does b0 tell us

what the response variable will be when our explanatory variable = 0

how to find b0

b0 = ybar - slopexbar

ybar = mean of all y values

slope = b1 = r x (sy/sx)

x bar = mean of all x values

what are scatterplots vs residual plots?

scatter = LSRL + o.g. values

residual = x axis is the explanatory variable in o.g. values, and the y axis is the residuals (so that value the y value - y with a v on top value, which is the predicted value by the LSRL)

what is an influential point?

any point if removed would change EITHER the y intercept or the correlation

what happens if you remove/add an influential point?

affects r and/or affects y intercept

what is homeoscadastic

ms. weatherspoon def: when the varaibility (spread) of residulas is approx constant across all values of explanatory variable 

simplified: so as you move along the x axis (as explanatory varaible increases) there isn’t a pattern for the residuals increasing or decreasing it remains random - like the residuals dont increase or decrease as the explanatory increases

what’s a good residual plot?

when the points are spreed = homeoscadastic

observational study def

record what happens naturally w/o intervention

experiment def

actively impose treatments on experimental units and observe the results

confounding variable def

a factor related to the explanatory varaiable that will influence the response variable

so like if you want to have a good experiment what do you have to make sure about your explanatory variable?

that confounding varaibles that are related to the explanatory varaubles which may influence the response variable are accounted for through some type of system (ex rbd, blocking, control)

experimental units def

people receiving treatment

treatment

what is done/not done to the exp. units

what are the steps for designing a good experiment?

1. comparison

2. RA (a) label, (b) randomize, © assign

3. replication

4. control

what is replication?

Replication means having many subjects in each treatment so your conclusion is more trustworthy.

me explaining: replication means like making sure you have a lot of test units for your experiment - bc the more people tested on the more legitimate your conclusion - so amount of test subjects/ exp. units

what is control?

control means controlling for other variables: so having a control group and/or blocking possible confounding variables

what is comparison?

being able to compare to sets of data (ie control group vs received treatment group)

RA meaning:

randomly assigning exp. units to treatment groups

placebo effect def

when a fake treatment “works” - conciousness infiltrated in

how do we prevent placebo

double/single blond study

single blind study def

exp. units dont know which treatment they are receiving

double blind study def

exp. units and researchers/ppl adminstering the treatments dont know which treatment they are receiving

what is RBD? (randomized block design)

grouping subjects into blocks based on a shared characteristic (which is a confounding variable) that may affect the response. RA exp. units treatments within each block

so if ms. weatherspoon asks how to draw diagram of completely randomized - what do you do?

name population - RA - exp. units r put into either control group or treatment group - compare the results

so if ms. weatherspoon asks how to draw diagram of RBD - what do you do?

name population (exp units) - split into confounding variables or their characteristic groups - RA in each block - the RA leads into control or treatment - compare the control and treament within each block - compare the two blocks data

ex is attached

what is matched pairs?

RBD where each block has exactly 2 exp units, the exp units r similar in some way - they receive diff treatments

so like twins are each block, each twin gets a diff treatment, the twins share 100% same of the dna

crossover def

each subject receives multiple treatments in sequence, but randomly assigned order

crf - completely randomized factorial

testing all treatments simultaneously and getting all possible treatment combos

rbd is similar to what type of grouping / organization

strata

how do u do this

plug into calc - gives you the LSRL line

how do you find a residual from this line?

calc what the predicted thing is by plugging in x into the equation you found

getting the y value for the x value from the data set 

y value - predicted value

in this photo - if i told you to make a equation - how would you do it?

so - only look at the first 2 values for constant and basal area

top one is the y value

bottom one is the slope

so it would be

y with a v on top = -12.36x + 148.32

REMEMBER top = y

bottom = slope

ONLY FIRST 2

reminder

blocking in situations with two exp units for each block does classify as matched pairs

reminder

it can only be an experiment if you’re ACTIVELY imposing treatments on the exp units