1. Data Preparation

2. Steps in Data Preparation
Editing
Coding
Entering Data
Data Tabulation
Reviewing Tabulations
Statistically adjusting the data (e.g. weighting)

3. Editing Carefully checking survey data for
Completeness (no omissions)
Non-ambiguous (e.g. two boxes checked instead of one)
Right informant (e.g. under age, when all supposed to be over 18)
Consistency
e.g. charging something on a credit card when the person does not own a credit card
Accuracy (e.g. no numbers out of range)
Most important purpose is to eliminate or at least reduce the number of errors in the raw data.

4. Solutions Ideally re-interview respondent
Eliminate all unacceptable surveys (case wise deletion) (if sample is large and few unacceptable)
In calculations only the cases with complete responses are considered (pair wise deletion) (means that some statistics will be based on different sample sizes)
Code illegible or missing answers into a a “no valid response” category
substitute a neutral value - typically the mean response to the variable, therefore the mean remains unchanged

5. Coding
The process of systematically and consistently assigning each response a numerical score.
The key to a good coding system is for the coding categories to be mutually exclusive and the entire system to be collectively exhaustive.
To be mutually exclusive, every response must fit into only one category.
To be collectively exhaustive, all possible responses must fit into one of the categories.
Exhaustive means that you have covered the entire range of the variable with your measurement.

6. Coding
Coding Missing Numbers: When respondents fail to complete portions of the survey.
Whatever the reason for incomplete surveys, you must indicate that there was no response provided by the respondent.
For single digit responses code as “9”, 2 digit code as “99”

7. Coding Open-Ended Questions: When open-ended questions are used, you must create categories.
All responses must fit into a category
similar responses should fall into the same category.
e.g. Who services your car? ______________
Possible categories: self, garage, husband, wife, friend, relative etc.
To make it collectively exhaustive add an “other” or “none of the above” category
Only a few i.e. < 10% should fit into this category

8. Precoded Questionnaires: Sometimes you can place codes on the actual questionnaire, which simplifies data entry.
This…
Becomes this…
Are you: Male Female
How satisfied are you with our product?
___Very Satisfied
___Somewhat Satisfied
___Somewhat Dissatisfied
___Very Dissatisfied
___No opinion
Are you: (1) Male (2) Female
How satisfied are you with our product?
_1__Very Satisfied
_2__Somewhat Satisfied
_3__Somewhat Dissatisfied
_4__Very Dissatisfied
_5__No opinion

9. Are you solely responsible for taking care of your automotive service needs ___ Yes ___ No
If No who performs the simple maintenance ___________
If scheduled maintenance is done on your automobile, how do you keep track of what has been done
 Not tracked
 auto dealer records
 mental recollection
 other
How often is your automobile serviced?
 Once per month
 Once every three months
 Once every six months
 Once per year
 Other _______________

10. Code Book Col. No Question No. Question Des.
Range of permissible values 1
ID #
N/A
(this also means the surveys themselves should be numbered) 2
Responsible for Maintenance
0= No. 1=yes, 9= blank 3
perform simple maintenance
0=husband, 1=boyfriend, 2=father, 3=mother, 4=relative, 5=friend, 6=other, 9=blank 4
How maintenance tracked
0=not tracked, 1=auto dealer records, 2=personal records, 3=mental recollection, 4=other, 9=blank 5
How often maintenance performed
1=Once per month, 2=3 month, 3=6 months , 4=year , 5=other, 9= blank

11. 6. Which magazines do you read, choose all that apply.
In questions that permit multiple responses, each possible response option should be assigned a separate column
6. Which magazines do you read, choose all that apply.
 Time  National Geographic
 Readers Digest  Chatelaine
 MacLean's
Col. No
Question No.
Question Des.
Range of permissible values 15 6
Time
0 =read, 1= not read 16
Readers Dig. 17
MacLean's 18
National Geo. 19
Chatelaine

12. For rank order questions, separate columns are also needed
7. Please rank the following brands of toothpaste in order of preference (1-5) with 1 being the most important
 Crest  Colgate
 Aquafresh  Arm & Hammer
 Aim
Col.#
Q. No.
Question Des.
Range of permissible values 20 7
Crest rank
0 =blank, 1 = most important, 2 =2nd most important, 3 =third, 4=fourth, 5= fifth 21
Colgate rank 22
Acquafresh rank 23
A & H rank 25
Pepsodent rank

13. Preparing the Data for Analysis
Variable Re-specification
Existing data modified to create new variables
Large number of variables collapsed into fewer variables
E.g. If 10 reasons for purchasing a car are given they might be collapsed into four categories e.g. performance, price, appearance, and service
Creates variables that are consistent with research questions

14. Entering Data
Problems can occur during data entry, such as transposing numbers and inputting an infeasible code(e.g out of range)
E.g. Score on range of 1-5 then 0, 6, 7, and 8 are unacceptable or out of range (might be due to transcription error)
Always check the data-entry work.

15. Descriptive Statistics

16. Five types of statistical analysis
What are the characteristics of
the respondents?
Descriptive
What are the characteristics of
the population?
Inferential
Are two or more groups the same
or different?
Differences
Are two or more variables related
in a systematic way?
Associative
Can we predict one variable if we know one or more other variables?
Predictive

17. Descriptive Statistics
Summarization of a collection of data in a clear and understandable way
the most basic form of statistics
lays the foundation for all statistical knowledge
Measures of central tendency
mean, median, mode
Measures of dispersion
range, standard deviation, and coefficient of variation
Measures of shape
skewness and kurtosis
If you use fewer statistics to describe the distribution of a variable, you lose information but gain clarity.

18. Proportion (percentage)
Type of
Measurement
Type of
descriptive analysis
Frequency table
Proportion (percentage)
Category proportions
(percentages)
Mode
Two
categories
Nominal
More than
two categories

19. Type of
Measurement
Type of
descriptive analysis
Ordinal
Rank order
Median
Interval
Arithmetic mean
Ratio
means

20. Data Tabulation
Tabulation: The organized arrangement of data in a table format that is easy to read and understand.
A count of the number of responses to each question.
Simple Tabulation: tabulating of results of only one variable informs you how often each response was given.
Frequency Distribution: A distribution of data that summarizes the number of times a certain value of a variable occurs expressed in terms of percentages.

21. Frequency Tables
The arrangement of statistical data in a row-and-column format that exhibits the count of responses or observations for each category assigned to a variable
How many of certain brand users can be called loyal?
What percentage of the market are heavy users and light users?
How many consumers are aware of a new product?
What brand is the “Top of Mind” of the market?

22. More on relative frequency distributions
Rules for relative frequency distributions:
Make sure each observation is in one and only one category.
Use categories of equal width.
Choose an appealing number of categories.
Provide labels
Double-check your graph.
A bar graph is a relative frequency distribution of a qualitative variable
A histogram is a relative frequency distribution of a quantitative variable

24. How many times per week do you use mouthwash ?
1__ 2__ 3__ 4__ 5__ 6__ 7__ 1 2 3 5 4 7 6

25. Normal Distribution 
-    a b

26. IQ
The total area under the curve is equal to 1, i.e. It takes in all observations
The area of a region under the normal distribution between any two values equals the probability of observing a value in that range when an observation is randomly selected from the distribution
For example, on a single draw there is a 34% chance of selecting from the distribution a person with an IQ between 100 and 115

27. Normal Distributions Curve is basically bell shaped from -  to 
symmetric with scores concentrated in the middle (i.e. on the mean) than in the tails.
Mean, medium and mode coincide
They differ in how spread out they are.
The area under each curve is 1.
The height of a normal distribution can be specified mathematically in terms of two parameters: the mean (m) and the standard deviation (s).
Normal Distributions

28. Skewed Distributions
Occur when one tail of the distribution is longer than the other.
Positive Skew Distributions
have a long tail in the positive direction.
sometimes called "skewed to the right"
more common than distributions with negative skews
E.g. distribution of income. Most people make under $40,000 a year, but some make quite a bit more with a small number making many millions of dollars per year
The positive tail therefore extends out quite a long way
Negative Skew Distributions
have a long tail in the negative direction.
called "skewed to the left."
negative tail stops at zero
E.g. GPA

29. Kurtosis: how peaked a distribution is
Kurtosis: how peaked a distribution is. A zero indicates normal distribution, positive numbers indicate a peak, negative numbers indicate a flatter distribution)
Peaked
distribution
Flat distribution
Thanks, Scott!

30. Dispersion or variability
Summary statistics
central tendency
Dispersion or variability
A quantitative measure of the degree to which scores in a distribution are spread out or are clustered together

31. Measures of Central Tendency
Mode: the number that occurs most often in a string (nominal data)
Median: half of the responses fall above this point, half fall below this point (ordinal data)
Mean: the average (interval/ratio data)

32. the most frequent category
Mode
the most frequent category
users 25%
non-users 75%
Advantages:
meaning is obvious
the only measure of central tendency that can be used with nominal data.
Disadvantages
many distributions have more than one mode, i.e. are “multimodal”
greatly subject to sample fluctuations
therefore not recommended to be used as the only measure of central tendency.

33. number times per week consumers use mouthwash
Median
the middle observation of the data
number times per week consumers use mouthwash
Frequency distribution of
Mouthwash use per week
Heavy user
Light user
Mode
Median
Mean

34. The Mean (average value)
sum of all the scores divided by the number of scores.
a good measure of central tendency for roughly symmetric distributions
can be misleading in skewed distributions since it can be greatly influenced by extreme scores in which case other statistics such as the median may be more informative
formula m = SX/N (population)
X = xi/n (sample)
where m an X are the population & sample means
and N and n are the number of scores.

35. Normal Distributions with different Means
-   1 2

36. Measures of Dispersion or Variability
Minimum, Maximum, and Range (Highest value minus the lowest value)
Variance
Standard Deviation (A measure’s distance from the mean)

37. - 1 SD
+ 1 SD
RANGE

38. Variance 2 = (x- xi)2/n ¯
The difference between an observed value and the mean is called the deviation from the mean
The variance is the mean squared deviation from the mean
i.e. you subtract each value from the mean, square each result and then take the average.
Because it is squared it can never be negative
2 = (x- xi)2/n

39. Standard Deviation S =  (x- xi)2/n ¯
The standard deviation is the square root of the variance
Thus the standard deviation is expressed in the same units as the variables
Helps us to understand how clustered or spread the distribution is around the mean value.
S =  (x- xi)2/n

40. Measures of Dispersion
Suppose we are testing the new flavor of a fruit punch
Dislike Like Data x
X= 4
2= 1
S = 1
2 = (x- xi)2/n
S =  (x- xi)2/n

41. Measures of Dispersion
Dislike Like Data x
X = 4.67
2=0.22
S = 0.47
2 = (x- xi)2/n
S =  (x- xi)2/n

42. Measures of Dispersion
Dislike Like Data x
X= 3
2=4
S = 2
2 = (x- xi)2/n
S =  (x- xi)2/n

43. Normal Distributions with different SD
-   1 2 3

44. Cross Tabulation
A statistical technique that involves tabulating the results of two or more variables simultaneously
informs you how often each response was given
Shows relationships among and between variables
frequency distribution for each subgroup compared to the frequency distribution for the total sample
must be nominally scaled

45. Cross-tabulation
Helps answer questions about whether two or more variables of interest are linked:
Is the type of mouthwash user (heavy or light) related to gender?
Is the preference for a certain flavor (cherry or lemon) related to the geographic region (north, south, east, west)?
Is income level associated with gender?
Cross-tabulation determines association not causality.

46. Dependent and Independent Variables
The variable being studied is called the dependent variable or response variable.
A variable that influences the dependent variable is called independent variable.

47. Cross-tabulation
Cross-tabulation of two or more variables is possible if the variables are discrete:
The frequency of one variable is subdivided by the other variable categories.
Generally a cross-tabulation table has:
Row percentages
Column percentages
Total percentages
Which one is better?
DEPENDS on which variable is considered as independent. .

48. Contingency Table
A contingency table shows the conjoint distribution of two discrete variables
This distribution represents the probability of observing a case in each cell
Probability is calculated as:
Observed cases
Total cases P=

49. Cross tabulation GROUPINC * Gender Crosstabulation 10 9 19 52.6% 47.4%
100.0%
55.6%
18.8%
28.8%
15.2%
13.6% 5 25 30
16.7%
83.3%
27.8%
52.1%
45.5%
7.6%
37.9% 3 14 17
17.6%
82.4%
29.2%
25.8%
4.5%
21.2% 18 48 66
27.3%
72.7%
Count
% within GROUPINC
% within Gender
% of Total
income <= 5
5>Income<= 10
income >10
GROUPINC
Total
Female
Male
Gender

50. General Procedure for Hypothesis Test
Formulate H0 (null hypothesis) and H1 (alternative hypothesis)
Select appropriate test
Choose level of significance
Calculate the test statistic (SPSS)
Determine the probability associated with the statistic.
Determine the critical value of the test statistic.

51. General Procedure for Hypothesis Test
a) Compare with the level of significance, 
b) Determine if the critical value falls in the rejection region. (check tables)
Reject or do not reject H0
Draw a conclusion

52. 1. Formulate H1and H0
The hypothesis the researcher wants to test is called the alternative hypothesis H1.
The opposite of the alternative hypothesis is the null hypothesis H0 (the status quo)(no difference between the sample and the population, or between samples).
The objective is to DISPROVE the null hypothesis.
The Significance Level is the Critical probability of choosing between the null hypothesis and the alternative hypothesis

53. 2. Select Appropriate Test
The selection of a proper Test depends on:
Scale of the data
nominal
interval
the statistic you seek to compare
Proportions (percentages)
means
the sampling distribution of such statistic
Normal Distribution
T Distribution
2 Distribution
Number of variables
Univariate
Bivariate
Multivariate
Type of question to be answered

54. Example
A tire manufacturer believes that men are more aware of their brand than women. To find out, a survey is conducted of 100 customers, 65 of whom are men and 35 of whom are women.
The question they are asked is: Are you aware of our brand: Yes or No. 50 of the men were aware and 15 were not, whereas 10 of the women were aware and 25 were not.
Are these differences significant?
Men Women Total
Aware
Unaware

55. 1. Formulate H1and H0
We want to know whether brand awareness is associated with gender. What are the Hypotheses
H0:
H1:
There is no difference in brand awareness based on gender
There is a difference in brand awareness based on gender
Chi-square test results are unstable if cell count is lower than 5

56. 2. Select Appropriate Test
X2 (Chi Square)
Used to discover whether 2 or more groups of one variable (dependent variable) vary significantly from each other with respect to some other variable (independent variable).
Are the two variables of interest associated:
Do men and women differ with respect to product usage (heavy, medium, or light)
Is the preference for a certain flavor (cherry or lemon) related to the geographic region (north, south, east, west)?
H0: Two variables are independent (not associated)
H1: Two variables are not independent (associated)
Must be nominal level, or, if interval or ratio must be divided into categories

57. Awareness of Tire Manufacturer’s Brand
Men Women Total
Aware 50/ /
Unaware / /
Estimated cell Frequency n C R E j i ij =
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size
Eij = estimated cell frequency

58. 3. Choose Level of Significance
Whenever we draw inferences about a population, there is a risk that an incorrect conclusion will be reached
The real question is how strong the evidence in favor of the alternative hypothesis must be to reject the null hypothesis.
The significance level states the probability of rejecting H0 when in fact it is true.
In this example an error would be committed if we said that there is a difference between men and women with respect to brand awareness when in fact there was no difference i.e. we have rejected the null hypothesis when it is in fact true
This error is commonly known as Type I error, The value of  is called the significance level of the test Type I error

59. Significance Level selected is typically .05 or .01
i.e 5% or 1%
In other words we are willing to accept the risk that 5% (or 1%) of the time the results we get indicate that we should reject the null hypothesis when it is in fact true.
5% (or 1%) of the time we are willing to commit a Type 1 error
stating there is a difference between men and women with respect to brand awareness when in fact there is no difference

60. 3. Choose Level of Significance
We commit Type error II when we incorrectly accept a null hypothesis when it is false. The probability of committing Type error II is denoted by .
In our example we commit a type II error when we say that.
there is NO difference between men and women with respect to brand awareness (we accept the null hypothesis) when in fact there is

61. Type I and Type II Errors
Accept null
Reject null
Null is true
Correct-
no error
Type I
error
Null is false
Type II
error
Correct-
no error

62. Which is worse?
Both are serious, but traditionally Type I error has been considered more serious, that’s why the objective of hypothesis testing is to reject H0 only when there is enough evidence that supports it.
Therefore, we choose  to be as small as possible without compromising . (accepting when false)
Increasing the sample size for a given α will decrease β (I.e. accepting the null hypothesis when it is in fact false)

63. Awareness of Tire Manufacturer’s Brand
Men Women Total
Aware 50/ /
Unaware / /
Estimated cell Frequency n C R E j i ij =
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size
Eij = estimated cell frequency

64. Chi-Square Test Estimated cell Frequency
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth column
n = sample size
Eij = estimated cell frequency
Chi-Square statistic
x² = chi-square statistics
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell
Degrees of Freedom
d.f.=(R-1)(C-1)

65. Degrees of Freedom
the number of values in the final calculation of a statistic that are free to vary
For example To calculate the standard deviation of a random sample, we must first calculate the mean of that sample and then compute the sum of the squared deviations from that mean
While there will be n such squared deviations only (n - 1) of them are free to assume any value whatsoever.
This is because the final squared deviation from the mean must include the one value of X such that the sum of all the Xs divided by n will equal the obtained mean of the sample.
All of the other (n - 1) squared deviations from the mean can, theoretically, have any values whatsoever..

66. Chi-Square Test: Differences Among Groups
4. Calculate the Test Statistic
Chi-Square Test: Differences Among Groups 21 ) 10 ( 39 50 2 - + = X 14 ) 25 ( 26 15 2 - +
161 . 22
643 8
654 4
762 5
102 3 2 = + c 1 ) )( ( - f d C R
Chi-square test results are unstable if cell count is lower than 5

67. 5. Determine the Probability-value (Critical Value)
The p-value is the probability of seeing a random sample at least as extreme as the sample observed given that the null hypothesis is true.
given the value of alpha,  we use statistical theory to determine the rejection region.
If the sample falls into this region we reject the null hypothesis; otherwise, we accept it
Sample evidence that falls into the rejection region is called statistically significant at the alpha level.

68. Critical value critical value Test statistic
A critical value is the value that a test statistic must exceed in order for the the null hypothesis to be rejected.
For example, the critical value of t (with 12 degrees of freedom using the .05 significance level) is 2.18.
This means that for the probability value to be less than or equal to .05, the absolute value of the t statistic must be 2.18 or greater.
critical value
Significance level (.05)
2.816
2.023
-2.023
/2
Test statistic

69. Significance from p-values -- continued
How small is a “small” p-value? This is largely a matter of semantics but if the
p-value is less than 0.01, it provides “convincing” evidence that the alternative hypothesis is true;
p-value is between 0.01 and 0.05, there is “strong” evidence in favor of the alternative hypothesis;
p-value is between 0.05 and 0.10, it is in a “gray area”;
p-values greater than 0.10 are interpreted as weak or no evidence in support of the alternative.

70. Chi-square Test for Independence
5. Determine the Probability-value (Critical Value)
Chi-square Test for Independence
Under H0, the probability distribution is approximately distributed by the Chi-square distribution (2).  2
Reject H0
3.84
22.16
Chi-square
2 with 1 d.f. at .05 critical value = 3.84

71. a) Compare with the level of significance, 
b) Determine if the critical value falls in the rejection region. (check tables)
22.16 is greater than 3.84 and falls in the rejection area
In fact it is significant at the .001 level, which means that the chance that our variables are independent, and we just happened to pick an outlying sample, is less than 1/1000
Or, in other words, the chance that we have a Type 1 error is less than .1%
i.e. That there is a .1% chance that we reject the null hypothesis when it is true -- that there is no difference between men and women with respect to brand awareness, and say that there is, when in fact the null hypothesis is true: there is no difference.

72. Reject or do not reject H0
Since is greater than 3.84 we reject the null hypothesis
Draw a conclusion
Men and women differ with respect to brand awareness, specifically, men are more brand aware then women