1-3 id id no. of respondents respon 1 responsible for maintenance? 1 = no, 2 = yes, 9 = blank

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1 Basic Data Analysis Graziadio School of Business and Management Data Preparation & Entry Editing: Inspection & Correction Field Edit: Immediate follow-up (complete? legible? comprehensible? consistent? uniform?) Office Edit: Establishing Policies Incomplete Answers Wrong Answers Lack of Interest: Subtle vs. Obvious ow to handle incomplete questionnaires depends on the severity of the problem Coding: Technical procedure by which raw data are transformed into symbols Step 1: Specifying the categories and classes Step 2: Assigning code numbers to the classes Step 3: Preparing a codebook that contains general instructions indicating how each item of data was coded Codebook: Particularly important for open-ended questions Numeric codes are better Don t forget ID numbers Be careful with missing values Codebook Column Variable Question number name number Brief Description Values 1-3 id id no. of respondents respon 1 responsible for maintenance? 1 = no, 2 = yes, 9 = blank 5 who 1 who is responsible? 1 = husband, 2 = wife, 3 = boyfriend, 4 = father, 5 = mother, 6 = relative, 7 = friend, 8 = other, 9 = blank 6 perform 2 perform maintenance? 1 = no, 2 = yes, 9 = blank 7 often 3 how often? Once per: 1 = month, 2 = three months, 3 = six months, 4 = year, 5 = other, 9 = blank 8 often2 3 other for how often 9 handle 4 when are problems handled? 1 = scheduled maintenance, 2 = as problems arise, 3 = postpone, 4 = other, 5 = not keep track, 9 = blank handle2 4 other for when problems are handled 12 tire 5 rank of importance: tire 1 = most important, 2 = second, 3 = third, 4 = fourth, 5 = fifth, 9 = blank 13 oil 5 rank of importance: oil change 1 = most important, 2 = second, 3 = third, 4 = fourth, 5 = fifth, 9 = blank 14 brake 5 rank of importance: brake maintenance 1 = most important, 2 = second, 3 = third, 4 = fourth, 5 = fifth, 9 = blank 15 belts 5 rank of importance: belts and hoses 1 = most important, 2 = second, 3 = third, 4 = fourth, 5 = fifth, 9 = blank 16 plugs 5 rank of importance: spark plugs 1 = most important, 2 = second, 3 = third, 4 = fourth, 5 = fifth, 9 = blank Variable Transformation Variable Re-specification: Collapsing into fewer variables

2 Data reduction Not recommended in the data-entry stage Scale Transformation: For comparability among variables When you want to compare sales with price Standardization is the most common technique: how? Weighting: Assigning some weights according to a pre-specified rule Do you have more important respondents? Be cautious Weighting should be explicitly reported Simple Data Analysis (1) Plots Why? To identify data errors and outliers (Data Cleaning); to find basic relationships; to provide a basis for evaluating more formal analysis; and most of all to understand your DATA! Scatter Plots EDUC INCOME Box Plots INCOME NUMCARS

3 (2) Descriptive Statistics INCOME Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness 3.85 Range Minimum Maximum Sum Count 100 Descriptive Analysis The transformation of raw data into a form that will make them easy to understand and interpret; rearranging, ordering, and manipulating data to generate descriptive information The first stage of analysis Descriptive Statistics Mean & Standard Deviation Frequency and Proportion (Percentage) Example: Research Question Assume that a marketing company is interested in market potential of a new product. Data includes two variables Gender(0/1), Purchase Intent(1-5) Example: Data In a small data set, you might observe its characteristics directly. In a large data set, it requires the use of software to analyze the data. (e.g., Excel, Minitab, SPSS...) Gender Purchase Intent

4 (3) One-Way Tabulation Tabulation - Orderly arrangement of data in a table or other summary format Frequency Table: 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 Easy to look for differences in certain subgroups in the sample. One-Way Tabulation Example 1. Frequency Table Gender Frequency Female 5 Male 5 Total 10 Example 2. Frequency Table Cars Per Family Number of Cars per family Number of Families Total 100 One-way Tabulation and istogram Count of ID INCOME Total < > Grand Total Cumulative %Cumulative INCOME #Families %Familes #Families #Families <= % 8 8.0% % % % % % % % % % % % % >= % % Total 100 <= >=105000

5 One-way Tabulation Purposes of One-way Tabulation To determine the degree item nonresponse To locate blunders To locate outliers or unusual observations To determine the empirical distribution To calculate summary statistics ow to deal with Nonresponse? Leave items blank and report the # as a separate category Eliminate the case with the missing item in analyses using the variables Substitute the values for the missing items (Mean ) A blunder is simply an error go back to the original questionnaire (e.g., 9 cars) Outlier is an observation so different in magnitude from the rest of the data Empirical distribution: Ignoring distribution of a variable can be a serious problem (e.g., Bipolar distribution of mild salsa and hot salsa) Statistical Methods in MR Five Types of Statistical Methods Descriptive analysis: used to describe the data set Inferential analysis: used to generate conclusions about the population s characteristics based on the sample data Differences analysis: used to compare the mean of the responses of one group to that of another group Associative analysis: determines the strength and direction of relationships between two or more variables Predictive analysis: allows one to make forecasts for future events

6 Sample Size Determination Sample Size Determination Statistical Factors: Standard Errors, Precision, Degree of Confidence Other Factors: Cross-classification, Budget Means vs. Proportions : half precision σ = z n zσ n = 2 2 z σ n = 2 π (1 π ) = z n z π (1 π ) n = 2 z π(1 π) n = 2 ypothesis An unproven proposition or supposition that tentatively explains certain facts or phenomena Null ypothesis ( o ): No change from the current position (default, status quo, skeptic s position) Alternative ypothesis ( a ): The claim that the investigator wants to show evidence of o and a are statements about population parameters The burden of proof is on the investigator to convince the skeptic to abandon the null hypothesis The rejection of the null hypothesis should lead to the acceptance of the desired conclusion Typical ypothesis Testing Procedure Specify Null and Alternative ypotheses after analyzing the research problem 2) Choose appropriate statistical test, considering research design, and sampling distribution for the test statistic 3) Specify the significance level (α) for the problem being investigated 4) Collect the data, compute the value of the test statistic appropriate for the sampling distribution 5) Determine probability of the test statistic under the null ypothesis using the sampling distribution in step 2 6) Compare the obtained probability with the specified significance level, reject or do not reject the null hypothesis on the basis of the comparison

7 Power & Two Types of Errors Power: the probability that you reject o when o should be rejected. i.e., how sensitive to detect the difference is the test Two types of error in hypothesis testing Type I Error: occurs when o is rejected, when in fact o is actually true. i.e., False positive e.g., Drug test in Olympic games 2. Type II Error: occurs when o is accepted, when in fact o is actually false. i.e., Medical test Types of Errors Truth o is true o is false Do not reject o Research conclusion Reject o Correct Type I Error (α) Type II Error (β) Correct e.g., o: Defendant is not guilty Type I error: Convict an innocent person Type II error: Guilty person is set free Which error is worse? Depends on the context and situation Type I error: More important in the American legal system Type II error: More important in a medical test Minimizing the Errors Ideally, we want the chance of each error to be zero. Unfortunately, when one is very small, the other is very large e.g., In the American leg al system, if we try to reduce type I error to zero, we would have huge type II error. Therefore, we should compromise by trying to make both of them reasonably small. The only way of reducing both errors simultaneously is to collect more data e.g., In a drug test case, test them again. In a legal case, allow more appeals Notation Pr(Type I error) = α = Significance level of the test (typically.05 or.01) If appeals are repeated twice, 0.05 * 0.05 getting smaller Pr(Type II error) = β Power = 1- β When Do We Use Normal (Z) or t Distribution?

8 large (>30) sample size? No Yes Normal Distribution (Calculating z-statistic) Population variance known? Yes No t Distribution (Calculating t-statistic; d.f. = n-1) Confidence Interval for Mean A restaurant owner is estimating ave. age of household heads of Pop. based on a sample n=400, δ = , and Construct Confidence Interval for Pop. Parameter Estimation CI = x ± Zδ or x ± Z X δ n = ± Calculating Test Statistic Z obs for Mean x µ x µ z obs = = δ δ n x / ypothesis Test mean =128

9 o : µ = 128 a : µ 128 α = σ X ~ N µ, n (Z obs ) > (Z crit ) Based on our sample, we cannot say that the population mean is different from µ= Decision Rule: When to Reject o? Test Statistics One-Sided Two-Sided (Tailed) Test (Tailed) Test (a: µ>µo or µ<µo (a: µ µo or or π>π or π <π) π π) Zobs>Zα or Zobs<-Zα tobs>tα, d.f.=n-1 or tobs<-tα, d.f.=n-1 Zobs>Zα/2 or Zobs<-Zα/2 P-value P-value < α P-value < α/2 SPSS P-value (Two-sided) (Sig.)/2 < α Sig. < α Confidence Interval for Proportion A restaurant owner is estimating Pop. Proportion for the subscribers of a certain magazine based on a sample n=400, and P = 45.3%. Construct Confidence Interval for Pop. Proportion Estimation

10 CI = P ± Zσ P or P ± Z P(1 P) n = ± Calculating Test Statistic Z obs for Proportion Example A firm is considering introducing a new product if at least 20% of pop. are expected to prefer it. n= 625, P=2.24 z obs = P π δ P = P π π ( 1 π ) / n