Unit 1: Qualitative vs. Quantitative Data Flashcards
What is statistics?
- = the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data
- The mathematical foundations of statistics were laid in the 17th century with the development of the probability theory (Pascal, de Fermat, Legendre)
- Statistics as a scientific discipline on its own emerged in the late 19th and early 20th century (Galton, Pearson, Fisher, Gosset, Neyman
Why do we need data/statistics?
Statistics are used in education to…
* Gather information (record keeping)
* Harvard: info about age of enrollment in undergraduate programs, the number of students in different houses, etc.
* Describe, manipulate, and analyze
* What is the average age of undergraduate students for each of the last 10 years?
* Has it been changing? By how much?
Quantitative research
Multiple measures (think “tests”)
* Does the score change?
* Is the score different between groups?
Qualitative research
- Focus groups
- Interviews
- Observations
What is a variable?
Something that can change
* Have different manifestations
* Vary between or within subjects
* Qualitative or Quantitative
Constants
Do not vary
Qualitative Variables (aka categorical variables)
iffer by categories (not amount)
* If there are numbers, the numbers represent a GROUP, it
does NOT have mathematical significance
Quantitative Variables
Measurable differences
examples of categorical variables
Nominal
Dichotomous
Ordinal
examples of continuous variables
Interval
Ratio
Nominal
Types/Categories
name) = numbers which are NOT rank ordered AND are NOT compared to one another with regard to value. (They may provide some sort of “order”, but are not ranked from “best” to “worst”) They merely identify.
?Examples?
-phone numbers
-room number
-number on restaurant receipt
-lottery ticket
?When are nominal numbers found in assessment?
-page numbers on IEP documents, reports, etc.
-question numbering on tests
-numbers given to students to protect their identities
-the number of the school attended (PS 4)
Dichotomous
Only 2 choices
Ordinal
Ratings where the distance between 2 “numbers” might not be consistently the same
(ordered) = CAN BE rank ordered from “best” to “worst” (or vice- versa) on a continuum but nominal cant be ranked
?When are ordinal numbers found in assessment?
-test scores for a class
-percentile ranks
-place in race/contest
Take a peek at the numbers below. They are possible test scores on a test. Is the difference between the 1st and 2nd ranked scores the same as the difference/magnitude between the 2nd and 3rd scores? (yes)
100 99 98 97 96 95 94 93 92 91 90 89 88….
Interval
Along a continuum. Distance between numbers: meaningful
& consistent
a ratio scale without a logical zero point (a score of zero may not mean “none”)
?Examples?
-0 degrees on a thermometer does not mean “no temperature”
(also, because of no logical zero point, we can’t say that 100 degrees is twice as hot as 50 degrees
-Latitude and longitude
?When do we see the interval scale in assessment? (Not very often)
-Some tests like the SAT…even if you make no marks on your test, you get a score of 14.
Ratio
A type of interval, but 0 means you don’t have any of that
variable (“true 0”)
the size of the difference between two adjacent possible points/scores is always the same.
?Examples?
-height and weight (the difference between 6’1” and 6’0” is the same as the difference between 5’3” and 5’4”)
The ratio scale also has a zero point that means “nothing” or “none”.
-0 lbs means that something is weightless
-0 feet of altitude means you are on the ocean surface (calm, no tide)
-rulers (measuring sticks, not leaders of countries)
?When do we see the ratio scale in assessment?
-number of correctly answered questions on a test (raw score)
(22 correct out of 25 questions is one better than 21 out of 25)
-% correct on a test (derived score)
(the difference between 12% & 16% = the difference between 94% & 98%
