MAR4613 Exam Wednesday at 12 30 in normal classroom Chapter 12 Analysis Interpretation Individual Variables Independently Data Analysis Key Considerations Data analysis hinges on 2 considerations about the variable to be analyzed 1 Is the variable to be analyzed by itself or in relationship with other variables Analysis involving individual variables is univariate analysis Analysis involving multiple variables is multivariate analysis 2 What level of measurement was used Nominal and ordinal measures are referred to as categorical measures since they are easily used to group respondents or objects into groups Interval and ratio measures are referred to as continuous measures since interval and ratio level measures are similar when it comes to analysis the mean is the most commonly calculated statistic for both types If you can answer these two questions data analysis is easy Basic Univariate Statistics Categorical Measures Frequency Analysis A count of the number of cases that fall into each of the response categories Percentages are very useful for interpreting the results of categorical analyses and should be included whenever possible Unless your sample size is very large it is characteristic to report percentages as whole numbers i e no decimals Researchers almost always work with valid percentages which are simply percentages after taking out cases with missing data on the variable being analyzed Note the difference between the Percent and Valid Percent columns in the previous table The column Percent includes percentages calculated using all respondents including those who didn t answer the questions 3rd column Valid Percent are percentages with the missing cases are excluded Although the number of missing cases in a frequency analysis should be indicated valid percentages are normally reported along with the count Cumulative Valid Percent merely totals the percentages from one row to the next This is the percentage of observations with a value less than or equal to the level Frequency Analysis indicated Communicate the results of a study via univariate categorical analysis Determine the degree of item nonresponse Identify blunders error that arises during editing coding or data entry Identify outliers valid observations that are so different from the rest of the observations that hey ought to be treated as special cases Determine the empirical distribution of a variable Confidence Intervals for Proportions Confidence interval A projection of the range within which a population parameter will lie at a given level of confidence based on a statistic obtained from a probabilistic sample Sampling has an impact on analysis Drawing a probability sample allows for the appropriate calculation of confidence intervals 1 To produce a confidence interval you need to calculate the degree of sampling error for the particular statistic To calculate sampling error for a proportion you need 3 pieces of info 1 z the z score representing the desired degree of confidence usually 95 confidence where z 1 96 2 n the number of valid cases overall for the proportion 3 p the relevant proportion obtained from the sample Confidence intervals are p sampling error p sampling error p the relevant proportion obtained from the sample Sampling error considers the desired degree of confidence z and the number of valid cases overall for the proportion n in addition to p population proportion The resulting value is also frequently called the margin of sampling error Example We saw that 80 of respondents were female p and the total number of valid cases in the sample was 222 n We would like to establish a 95 confidence level z 1 96 What is the sampling error for proportion 1 96 square root of 0 80 1 0 80 222 0 05 What is the confidence interval 0 80 0 05 0 80 0 05 Thus we can be 95 confident that the actual proportion of women in the population lies between 0 75 and 0 85 inclusive If they want a narrower confidence interval greater precision they can decrease the degree of confidence desired at 90 confidence z 1 65 or increase sample size Basic Univariate Statistics Continuous Measures Descriptive Statistics Statistics that describe the distribution of responses on a variable The most commonly used descriptive statistics are the mean and standard deviation The mean pronounced x bar is a measure of central tendency Although mean values can be calculated for nay variable in a data set they are only meaningful for continuous interval ratio measures The mean is only useful with equal interval scales one of the common characteristics of interval and ratio measures The standard deviation s is measure of dispersion measure of the variation of responses on a variable Sometimes it is useful to convert continuous measures interval or ratio level to categorical measures nominal or ordinal level This is legitimate because measures at higher levels of measurement in this case continuous measures have all the properties of measures at lower levels Why do this Ease of interpretation for managers Two box Technique A technique for converting an interval level rating scale into a categorical measure for presentation purposes usually reported The percentage of respondents choosing one of the top two positions on a rating scale is Converting from continuous to categorical measures results in the loss of information about a variable To be safe always perform data analysis using the continuous version of a variable A simple solution for many univariate analyses is to provide both types of results 2 Basic Univariate Statistics Continuous Measures Two Box Technique How important to you personally is each of the following reasons for participating in Avery Fitness Center programs The Two Box column is the addition of the two right most boxes from the top table Confidence Intervals for Means A projection of the range within which a population mean will lie at a given level of confidence Managers care more about the population than they do about any particular sample As a result our job is to make projections about where the population mean is likely to fall rather than be satisfied with the sample mean Confidence intervals are x sampling error x sampling error x the sample mean Sampling error considers the desired degree of confidence z the sample standard deviation s and the number of valid cases overall for the sample n population mean As with proportion to establish the confidence interval we must estimate the degree of sampling
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