Target group for inference

The numerical characteristics of a population are

parameters

population mean = M(mew)

Large, unobtainable, often hypotehtical 

Subgroup of population

Numerical Characteristics are statistics

Sample mean is X bar

Obtainable, small, not hypothetical 

sample (infer)> ________

_______ (infer)> parameter 

population

statistic 

1. Use of a descriptive stat

2. use of probability

3. stat has a sampling variability

4. use of a theoretical distribution

6. stat has a sampling distribution

7. 2 hypotheses, 2 decisions, 2 types of errors

1. Encounter and identify the problem

2. Formulate hypotehsis/Define variables

3. Think through consequences of hypotehsis

4. Design study, run it, collect data, compute data, test hypotheses.

5. Draw conclusions 

It is manipulated by the researcher

Researcher changes the values of the variable

IV --->(time) DV

measured by the researcher

follows the IV in time 

SHOULD be controlled by the researcher

competitor to the IV

invluences DV 

1. Randomization of subjects to groups

2. keep all subjects constant on EV

3. Include EV in the design 

Follows PV in time

Analogous to the DV 

Causal Relationship

between variables

What causes what

3 keys 

IV causes DV

Keys:

1. Manipulation of an IV

2. Randomization of subjects to groups

3. Replication - N (# of groups) has to be greater than 1 

Predictive Relationships

of variables

What predicts what

3 keys 

PV predicts CV

Keys:

1. No Manipulation

2. No randomization of subjects to groups

3. Replication 

True Experiment

3 keys 

1. Manipulation

2. Randomization

3. Replication

Observational Research

3 keys 

Same as a predictive relationship

1. no manipulation

2. no randomization

3. replication 

Stem and Leaf display

One stem per digit 

Stem     Leaf

3       4788 

2          36

1          

0         9 

STem and Leaf Display

Two stems per digit 

Stem    Leaf

3.    788

3*    4

2.     6

2*     3

1.    

1*      

0.      9

Falling star (always last one) 

Stem and Leaf display

Five stems per digit 

Stem    Leaf

same format

.8-9

s 6-7

f 4-5

t 2-3

* 0-1 

Different aspects (characteristics) of data

Basically alternate names 

Middle 

Different aspects (characteristics) of data

Basically alternate names

Spread 

variability, dispersion

Different aspects (characteristics) of data

Basically alternate names

Skewness 

Different aspects (characteristics) of data

Basically alternate names

Kurtosis 

Statistics

measures/ describes:

 Middle

Statistics

measures/ describes:

 spread

Statistics

measures/ describes:

 skewness

NO STATISTICS

"The few name the skew"

Statistics

measures/ describes:

 Kurtosis

No stats

curved shape = middle

peaked shape = high

flat shape = low 

T20 is the 20% trimmed mean

Put the scores in order, trim (ignore) 20% of the scores in each tail, remaining middle 60%  compute an avg/mean

1 1 1|2 3 3 3 4 4 4 4 6|9 10 11 

add 2-6 equalling 33, divide by 9 to get T20 

1. state = 0, if spread is zero

2. As spread increases, stat increases

3. Stat measures just spread, not middle 

Midrange (MR)

Formula 

Midrange

UH-LH

Upper Hinge

Lower Hinge 

Computing the hinges

Use the Hinge position formula 

HP = ([MP] +1)/2

MP = (N+1)/2

When using Hinge Postion, count in from the ends to find the L+U hinge 

sample variance

∑(x-xbar)²/N

Is in squared units of measure 

sample standard deviation

S*=√S*²

S* is in original units of measure 

Unbiased variance estimate

A better estimate of σ² (Population variance)

S^{2 =} s(x-xbar)²/N-1

Observational Research --------------True Experiment

      ν

Quasi-Experimental Research

3 keys 

1. Has manipulation

2. Missing randomization

3. Has replication 

Box Plots

What is in the box?

What are the whiskers? 

box -

Upperend - UH

Middle - x₅₀

Lowerend - LH

Contains middle 50% of the data 

Whiskers-

lines drawn from a hinge to an adjacent value 

Not on box plot

UH+1.5MR

Midrange formula = UH-LH 

Formula: LH - 1.5MR

Midrange formula = UH-LH 

-Any real data values outside whiskers (adjacent values,fence)

-would mark individually w/ *