0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Quants

688

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
688
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
20
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. What is a Variable?
any entity that can take on different values
not always 'quantitative' or numerical, but we can assign numerical values
attribute = a specific value of a variable
Examples:
gender: 1=female; 2=male
attitudes: 1 = strongly disagree; 2 = disagree; 3 = neutral; 4 = agree; 5 = strongly agree
• 2. Coding in a data matrix
• 3. Coding in a data matrix
Gender: Male = 1; Female=2
Social Class: Working=1; Upper working=2; Lower middle=3; Middle=4; Upper middle=5
• 4. Levels of Measurement
different kinds of variables
(1) Nominal
(2) Ordinal
(3) Interval and Ratio
• 5. Nominal Variable
used to classify things
represents equivalence (=)
adding, subtracting, multiplying or dividing nominal numbers is meaningless
tells you how many categories there are in the scheme
• 6. Ordinal Variable
ordering or ranking of the variable
the relationship between numbered items
‘higher’, ‘lower’, ‘easier’, ‘faster’, ‘more often’
equivalence (=) and relative size (greater than) and < (less than)
• 7. Interval (and Ratio) Variable
All arithmetical operations are allowed
intervals between each step are of equal size
Examples:
• length, weight, elapsed time, speed, temperature
• 8. Levels of measurement

• 9. Frequency distributions
count number of occurrences that fall into each category of each variable
allow you to compare information between groups of individuals
also allow you to see what are the highest and lowest values and the value at which most scores cluster
variables of any level of measurement can be displayed in a frequency table
• 10. Frequency table
• 11. Percentages
number of cases belonging to particular category divided by the total number of cases and multiplied by 100.
the total of percentages in any particular group equals 100 per cent.
• 12. Graphical presentation
Pie charts
Barcharts
Line graphs
Histograms
• 13. Pie chart
illustrates the frequency (or percentage) of each individual category of a variable relative to the total.
Pie charts are not appropriate for displaying quantitative data.
• 14. 15
Barcharts
the height of the bar is proportional to the category of the variable - easy to compare
used for Nominal or Ordinal level variables (or discrete interval/ratio level variables with relatively few categories)
• 15. Multiple barchart
• 16. Compound or Component barchart
• 17. Line graphs
interval/ratio level variables that are discrete
need to arrange the values in order
• 18. Histograms
represents continuous quantitative data
The height of the bars corresponds to the frequency or percentage of cases in the class.
The width of the bars represents the size of the intervals of the variable
The horizontal axis is marked out using the mid points of class intervals
• 19. Example: Histogram
• 20. Graphs have the capacity to distort
• 21. Measures of Central Tendency
describe sets of numbers briefly, yet accurately
describe groups of numbers by means of other, but fewer numbers
Three main measures:
mean
median
mode
• 22. The Mean
• most common type of average that is computed.
• When to use the Mean
When values in a particular group cluster closely around a central value, the mean is a good way of indicating the ‘typical’ score, i.e. it is truly representative of the numbers.
If the values are very widely spread, are very unevenly distributed, or clustered around extreme values, than the mean can be misleading, and other measures of central tendency should be used instead.
• 23. The Median
Also an average, but of different kind.
It is defined as the midpoint in a set of scores. It is the point at which one-half, or 50% of the scores fall above and one-half, or 50%, fell below.
Computing the Median:
(1) List the scores in order, either from highest to lowest or lowest to highest.
(2) Find the middle score. That’s the median.
• 24. The Median: Pros and Cons
time-consuming
if one of the numbers near the middle of the distribution moves even slightly, than the median would alter, unlike the mean, which is relatively unaffected by a change in one of the central numbers
if one of the extreme values changes, than the median remains unaltered.
• 2, 80, 100, 120, 130, 140, 160, 200, 3150
single scores which are quite clearly ‘deviant’ when compared with others, are known as outliers – 2 and 3150
• 25. The Mode
the value in any set of scores that occurs most often
example 1:
5, 6, 7, 8, 8, 8, 9, 10, 10, 12 – the mode = 8
example 2:
5, 6, 7, 8, 8, 8, 9, 10, 10, 10, 12 –two modes: 8 and 10 – bimodal
very unstable figure
1,1,6,7,8,10 – mode = 1
1,6,7,8,10,10 – mode = 10
• 26. When to Use What?
depends on the type of data that you are describing
for nominal data - only the mode
for ordinal data - mode and median
for interval data - all of them
but, for extreme scores - use the median
• 27. Measure of dispersion (spread)
better impression of a distribution’s shape
measures indicate how widely scattered the numbers are
how different scores are from one particular score – the mean
variability - a measure of how much each score in a group of scores differs from the mean
• 28. The range
tells us over how many numbers altogether a distribution is spread
• where
• 29. r is the range
• 30. h is the highest score in the data set
• 31. l is the lowest score in the data set.
• r = biggest value - smallest value = 55-10 = 45
• 32. The mean deviation
number which indicates how much, on average, the scores in a distribution differ from a central point, the mean.
Mean deviation =
• 33. 210
368
364
319
-210
-368
-319
-364
Mean=370
X - mean= (-210)+210+(-368)+368+(-364)+364+(-319)+319 = 0
X - mean= 210+210+368+368+364+364+319+319 = 2522
mean deviation = 2522/8 = 315.25
• 34. The standard deviation (SD)
represents the average amount of variability
It is the average distance from the mean
• sthe standard deviation
• 35. find the sum of what follows
• 36. Xeach individual score
• 37. the mean of all the scores
• 38. Nthe sample size
• Standard deviations
• 39. Shape of Normal Distribution
Symmetrical
Asymptotic tail
Mean
Median
Mode
• 40. The area under the curve
A normal distribution always has the same relative proportions of scores falling between particular values of the numbers involved.
Areas under the curve = proportion of scores lying in the various parts of the complete distribution
• 41. SS2008N - Surveys
Median
50%
50%
Median
• 42. SS2008N - Surveys
Quartiles
25%
25%
25%
25%
Median
Quartile 1
Quartile 3
• 43. Standard Deviation