Course Agenda

1
Course Agenda

• About One Chapter per week
• First Quiz Feb 7th (Chapters 1-3)
• First Homework Feb 21st
• Will be posted this weekend
• Work periodically (not all at once)
• Need access to SPSS

2
TECH Account

• Swipe UNM ID - TEC account
• Access to SPSS
• Instructor Folder

3
Practice Sets

• Good Work!
• Score of 10 - 1622 or 16/22 or 73
• MUST turn in practice set during class to
  receive credit.

4
Last day to add or change sections (yellow card)
required, if section is closed).

• 16 week term - Friday, January 27
• First 8-week term - Friday, January 20

5
Chapter 2

• Notation (Summation)
• Measurement (scales)
• Some rules for hand calculation
• Ratios, frequencies, percentage

6
Notation

• X an observation
• i a case or unit (person, classroom, school,
  etc)
• j a variable
• N Total number of cases in a set
• å summation sign

7
Formula for Sum
8
SUM (addition)

• Using an addition equation would look like this
• 2 3 5 8 6 9 7 2 6 12 2 3 5 8 9
  5 8 6 9 7 2 6 12 5 8 6 9 7 2 6
  12 ?
• The summation equation is more compact

9
Summation

• i takes on successive values beginning with i1
  ending with n (in 1)
• 2, 5, 6, 8, 1 22

Xs
10
Summation

• Limits of the summation
• Begin with the value of i (here it is the second
  case)
• End with the value 4 (or the fourth case)
• 5 6 8 19

11
Summation

• Often the notation above and below the sum sign,
  and the j (variable) subscript are absent.
• When absent it is assumed to sum from i 1 to N
  for a single variable.

12
Often EncounteredSummation Notation

• ? X ?
• 2 4 6 12
• ? Y ?
• 1 2 3 6
• (? X)² ?
• 2 4 6 12
• 12² (12 12)
• 144

• (? Y)² ?

13
Often EncounteredSummation Notation

• ? X² ?
• 2² 4² 6²
• 4 16 36 56
• ? Y² ?
• 1 4 9 14

14
Know the Difference

• (? X)² ?
• (2 1 4)²
• 7² 49
• ? X² ?
• 2² 1² 4²
• 4 1 16
• 21

15
Other EncounteredSummation Notation

• ? XY
• (21) (42) (63)
• (2 8 18)
• 28
• (? X) (? Y) 
• (12) (6)
• 72

16
MeasurementAssignment of numbers

• Nominal name
• Ordinal name order
• Interval name order equal interval (zero is
  arbitrary)
• Ratio name order equal interval true zero

17
Nominal

• Values are categories
• Example variable dog breeds
• Values collie (1) bulldog (2) poodle (3)
• Math operations (add, subtract, etc.) pointless
• While 1 2 3 6
• collie bulldog poodle ?
• Can count and compare ( ? ? NOT ? ?) categories
• 3 collies, 3 bulldogs
• collies bulldogs

18
Ordinal

• Values are categories and are ordered
• Example variable grade level
• first (1) second (2) third (3)
• Math operations again pointless
• 1 1 2
• However two first graders dont add up to a
  second grader
• Math comparisons (? ? ? ?) are possible.
• First ? Third

19
Interval and Ratio
20
Interval

• Values are categories, ordered, with equal
  intervals (zero arbitrary)
• Example variable Standardized score
• Zero average (above and below -)
• Math operations are possible
• 1 and 1 zero (average)
• However, ratio is not possible since zero is
  arbitrary

21
Ratio

• Categories, ordered, equal intervals with true
  zero.
• Example variable Height in inches
• 12 inches 12 inches zero height
• 24 inches twice as high as 12 inches
• 24/12 2/1 2

22
Transformed ScaleHigher ordered scales can be
transformed to lower order (but not reverse).

• Example Ratio scale variable height (inches)
  may be transformed to
• Interval scale by assigning values that differ
  from average (-2 1 0 1 2)
• Or ordinal Scale by assigning ordered categories
  (small, medium large)
• Or nominal scale by assigning named categories
  (tall short)

23
Big PictureInterpretation

• Math operations not appropriate for nominal and
  ordinal scales.
• Therefore
• Values for gender (male 1, female 2) cannot be
  averaged
• Second grade children are not twice as smart as
  first grade children.

24
Interpretation

• Math operations are possible for interval and
  ratio scales.
• However, only a ratio scale allows one to make
  proportional comparisons.
• Example 5 mm ½ (10mm)
• Interval scale does not allow such comparisons

25
X ChildInches ratioTrans interval
Zero inches no measurement of height Zero
trans ? 0 height
26
ContinuousDiscrete

• Discrete (discontinuous) assume no intermediate
  values.
• Family members, deaths, pregnancies etc.
• Partial values not possible (.5 children, almost
  dead, etc.)
• Continuous intermediate values unlimited
  (limited by measurement devise)
• Time (221216.004)

27
True Limits

• Continuous unlimited intermediate values
• True limits plus/minus ½ unit of measurement.
• Unit of measurement examples
• 4, 5, 6 the unit 1 and half a unit .5
• 4.5, 5.1, 6.3 unit .1 and half a unit .05
• 4.55, 5.26, 6.25 unit .01 and half .005

28
Rounding

• Hand calculation retain at least 6 significant
  decimals throughout all calculations
• example 12.123456 all six
• 12.12345000 retain 12.12345
• Round to two significant decimals ONLY for the
  FINAL answer (see rules p.39)
• 12.23500001 12.24 (greater than 5)
• 12.23442356 12.23 (less than 5)
• 12.22500000 12.22 (exactly 5 but even)
• 12.23500000 12.24 (exactly 5 but odd)

29
RatioProportion

• Ratio Part/whole comparison
• Ratio expressed as a comparison 2050 (or 20 to
  50 or 2 to 5 or 2/5)
• Proportion expressed in relation to 100s often
  as a decimal .40 (40 in 100)
• Percentage proportion X 100 or 40

30
Practice Set 2

• Collaborate with peers.
• Complete work by 600 p.m. (or sooner)
• Review will start at 600 or when all turn in
  their work
• Whichever occurs first