1. Introduction to Statistics & Measurement
Lecture 1
Homework
Ch 1: 1-3,6-8; Ch 2: 1-4, 6, 8, 10

2. Types of Statistics Descriptive organize summarize Inferential
drawing a conclusion about a group
based on data from subgroup ~

3. Domain of Statistics
What type of statements can be assessed by statistics?
Inductive statements
truth can be assessed by collecting and analyzing data
data > conclusion
(specifics) (generalization) ~

4. Experimental/Statistical Method
Characteristics
1. Inspiration comes from observations
2. Interested in whole group
e.g., all college statistics students
not just small group
3. Meaningful results from fluctuating data ~

5. Samples from Populations
Population: all members of group
size depends on our interest
Usually impractical to assess population
Parameter: measure from population
Sample = subset of population
representative of population
Statistic: any measurement from a sample ~

6. Variables & Measurement
Variable: any measurable characteristic
and can take on many different values
can assign arbitrary values
Measurement:
procedure for assigning values to a variable
must be mutually exclusive
unambiguous result for each individual ~

7. Levels of Measurement 4 types of variables & measurement levels
Nominal scale
qualitative: do not represent magnitudes
order NOT important
Ordinal scale
have a logical order
qualitative: undefined distance between
If assign numerical value, must reflect order ~

8. Levels of Measurement Interval scale - quantitative
requires logical order
width of all categories must be equal
Ratio scale
same characteristics as interval
scale must have true zero point
Interval/ratio treated same for course
nominal, ordinal, interval/ratio distinction important
some statistics not relevant for a scale ~

9. Discrete & Continuous Variables
no possible intermediate points b/n adjacent values
integers, counting numbers
e.g., # of children in family
Nominal level: always discrete ~

10. Discrete & Continuous Variables
Ordinal & interval/ratio can be discrete OR continuous
Continuous variable
has infinite number of values b/n adjacent scale values
e.g., height, weight, temperature
review in text
rounding rules
significant figures ~

11. Notation Assign symbol to variable name convenience, shorthand
Most common: single variable = X
2 variables: X and Y
3 variables: X, Y, and Z
or other logical symbols: height = H ~

12. Notation Data set set of measurements of variable(s)
each measurement = a data point
Index variable
particular measurement’s position in data set
i = 1 refers to the first subject
i = 2, the second subject, etc
order is usually arbitrary ~

13. Notation n = # of measurements in sample e.g. n = 5
Use subscript when referring to specific data point
Xi = i th value of X
X2 = 2d value of X ~

14. Summation Notation S Xi = X1 + X2 + X3 + X4 + X5
Often sum data points in set
S means to summate
S Xi = X1 + X2 + X3 + X4 + X5
shorthand: S Xi = X1 + X X5

15. Computations S X2i = X21 + X22 + X23 + X24 + 2X5 ~
Sometimes need to perform calculations before summation
e.g., S 3X
= 3X1 + 3X2 + 3X3 + 3X4 + 3X5
S X2i = X21 + X22 + X23 + X24 + 2X5 ~

16. Computations: Suggestion
Box 2.2, pp. 18,19
Do calculations one step at a time
e.g., S 3X2
1st find X2 for each data point
then make new column multiply by 3
fewer mistakes
easier to find mistakes ~

17. Computations: Suggestion1 2 3 4 5 X 2 1 3 X2
3X2 4 12 4 12 1 3 9 27 4 12 S 66

18. Computations
S X2i versus (S Xi)2
SXY versus SX SY
SX + 1 versus S(X + 1) ~