Marketing Research Final CHAPTER 12 ANALYSIS AND INTERPRETATION INDIVIDUAL VARIABLE INDEPENDENTLY Data Analysis Key Considerations Is the variable to be analyzed by itself or in relationship with other variables o Analysis involving individual variables is univariate analysis o Analysis involving multiple variables is multivariate analysis What level of measurement was used o Nominal and ordinal measures are referred to as categorical measures Male or female nominal Highest level of education achieved ordinal o Interval and ratio measures are referred to as continuous measures Basic Univariate Statistics Categorical Measures Frequency Analysis a count of the number of cases that fall into each of the response categories Incredibly important and commonly used to report the overall results Percentages are very useful for interpreting the results of categorical analyses and should be included whenever possible o Unless your sample size is large it is characteristic to report percentages as whole numbers 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 o Difference between percent and valid percent columns on exhibit o cumulative valid percent totals the percentages from one row to the 12 1 next Frequency Analysis Communicate the results of a study via univariate categorical analysis Determine the degree of item nonresponse Identify blunders Identify outliers valid observations that are so different from the rest of the observations that they ought to be treated as special cases May mean eliminating the observation from the analysis or trying to determine why this case is so different o Histogram a form of a bar chart that is based on information from a frequency count Determine the empirical distribution of a variable It is useful to identify the median point as a measure of average for the distribution Confidence Intervals for Proportions A projection of the range within which a population parameter will lie at a given level of confidence based on a statistic obtained from the probabilistic sample o Sampling has an impact on analysis o Drawing a probability sample allows for the appropriate calculation of confidence intervals To produce a confidence interval you need to calculate the degree of sampling error for the particular statistic Confidence intervals are p sampling error p sampling error o To calculate sampling error for a proportion we need 3 things o The z score representing the desired degree of confidence usually 95 confidence z 1 96 o n the number of valid cases overall for the proportion o p the relevant proportion obtained from the sample o population proportion o 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 establish a 95 confidence level z 1 96 What is the sampling error for proportion o 1 96 square root of 8 1 8 222 05 o What is confidence interval 80 05 80 05 o We can be 95 confident that the actual proportion of women in the population lies between 75 and 85 inclusive Basic Univariate Statistics Continuous Measures Because interval and ratio level measures are similar when it comes to analysis the mean is the most commonly calculated statistics for both types researchers refer to them as continuous measures even the label is not technically correct especially for interval measures such as ratings scales Descriptive Statistics statistics that describe the distribution of responses on a variable including measures of central tendency mean median and mode and various measures of the shape of the distribution skewness kurtosis The most commonly used descriptive statistics are the mean and standard deviation o The sample mean pronounced x bar is a measure of central tendency Sum the age values across respondents and dividing by the total number of valid cases Only useful for continuous measures Round to a whole number When there are outliers either report the median value or ignore the outliers and calculate the mean across the remaining cases o The standard deviation s is a measure of dispersion It provides a measure of the variation in responses for continuous measures 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 have all the properties of measures at lower levels Why Ease of interpretation for managers Cumulative percentage breakdown a technique for converting a continuous measure into a categorical measure The categories are formed based on the cumulative percentages in frequency analysis Median split a case on the cumulative percentage breakdown Used if you want to convert a continuous measure into 2 approximately equal sized groups The cumulative percent column of the frequency analysis output will identify a value at the 50th percentiles and values up to and including this value will for one group low group for ratio measures and values above the median value will form the second group high group Two box technique a technique for converting an interval level rating scale into a categorical measure for presentation purposes The percentage of respondents choosing one of the top two positions on a rating scale is usually reported A projection of the range with which a population mean will lie at a given x sampling error x sampling error Confidence Intervals for Means level of confidence Confidence intervals are the sample mean population mean x Researchers learned that the average number of visits to Avery Fitness over the last 30 days was 10 visits with a standard deviation of 7 3 from 198 responding members 95 confidence interval z 1 96 What is the sampling error for means 1 96 7 3 square root of 198 1 0 What is the confidence interval 10 1 We can be 95 confident that the mean number of visits to the fitness center 10 1 in the past 30 days lies between 9 and 11 inclusive Hypothesis Testing How can we tell if a particular result in the sample represents the true situation in the population or simply occurred by chance Null Hypothesis Ho the hypothesis that a proposed result is not true for the population Researchers typically attempt to reject the null hypothesis in favor of some alternative hypothesis Alternative Hypothesis Ha the hypothesis that a proposed result is true for the population Significance level alpha 05
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