Radford MKTG 446 - One-Way Tabulation

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Copyright, Angela D’Auria Stanton, Ph.D., 2007. All Rights Reserved. Page 1 ONE-WAY TABULATION This represents the most basic tabulation. It goes by various names including marginal tabulation, one-way tabulation and the frequency distribution. It consists of a simple count of the number of responses that occur in each of the data categories that comprise a variable. We run one-way tabulations in order to:  determine the degree of non-response  locate blunders  locate outliers  determine the empirical distribution of the variable in question  calculate summary statistics StatisticsSealtest: Fresh Taste264433.063.0031.171.38-.082.150-.762.299415807ValidMissingNMeanMedianModeStd. DeviationVarianceSkewnessStd. Error of SkewnessKurtosisStd. Error of KurtosisRangeMinimumMaximumSum Sealtest: Fresh Taste30 9.8 11.4 11.452 16.9 19.7 31.187 28.3 33.0 64.063 20.5 23.9 87.932 10.4 12.1 100.0264 86.0 100.043 14.0307 100.0Does Not Describe Well234Describes WellTotalValidSystemMissingTotalFrequency PercentValidPercentCumulative Percent Measures of central tendency Measures of dispersion/variation Number of people who responded or provided data Number of people who did not answer or provide data Shape of the distribution Variable label (name) Frequency divided by total # of respondents who provided data (does not include missing values) Sum of the valid percent and all rows before it Frequency divided by total # of respondents Count - # of times response chosen Value label Values Total # of respondents Number of people not answering question Total # people who answered questionCopyright, Angela D’Auria Stanton, Ph.D., 2007. All Rights Reserved. Page 2 A Review of Descriptive Statistics Measures of Central Tendency The measure of central tendency is a report of the “average” response. That is, the most typical response, or a person’s “best guess” of someone picked at random from the population sampled would respond. The measure you use depends upon the type of scale data (remember the charts for choosing the appropriate analytical technique). The three most commonly used measures of central tendency are: • Mode o The mode is simply the category or value with the greatest frequency of cases. It is used to describe the most typical case for nominal data. • Median o The median value is the preferred measure of central tendency for ordinal data. In a sample with an odd number of cases, the median is the middle observation when the data values are ordered from smallest to largest. When the sample size is even, the median is the average of the two middle values. o Since it’s merely the middle value, the median isn’t affected by extreme values of the existence of outliers. To put it another way, the middle value or median will be the same, no matter how much greater or lesser the values of the extremes turn out to be. Consequently, the median is likely to be more typical of the majority of cases and a better average to use than the mean with asymmetrical distributions where there are outliers. • Mean o The mean is the arithmetic average. o It is the most common average used to indicate the most typical response. While the median and the mode can also be used to describe central tendency for interval or ratio data, the mean is usually the most meaningful statistic. It is computed by dividing the sum of the values by the number of values or cases. It is not appropriate for nominal or ordinal data. o The mean tends to be overly sensitive to influence by only one or a few extreme values in the distribution (outliers) – meaning an extremely low value (or values) can lower the mean and an extremely high value (or values) can raise the mean. With outliers, the mean isn’t very typical of either the vast majority of cases or of the outliers. When this occurs, most people use the median (or sometimes the mode) in place of the mean.Copyright, Angela D’Auria Stanton, Ph.D., 2007. All Rights Reserved. Page 3 A Review of Descriptive Statistics Measures of Dispersion/Variation Measures of central tendency provide information only about “typical” values. They tell you nothing about how much the values vary within the sample. Measures of dispersion describe how close to the measure of central tendency the rest of the values in the distribution fall. The most commonly used measures of dispersion include: • Range o The range identifies the distance between the lowest value (minimum) and the highest value (maximum) in an ordered set of values. It shows the extent of the spread between extremes. The range provides some information on the dispersion by indicating how far apart the extremes are found (it’s basically the width or spread of the distribution). • Variance and Standard Deviation o Variance and standard deviation are measures of dispersion that permit a person to estimate a report the proportion of respondents or cases within certain ranges in the center part of the distribution, as well as toward the extremes, providing that the distribution doesn’t deviate very markedly from the normal, bell-shaped curve. o The variance and standard deviation are measures of the deviation or spread away from the mean. It’s a single value that indicates the amount of spread in a distribution, or the average distance of the distribution values from the mean. o The standard deviation (the square root of the variance) allows you to obtain a measure in the same units as the original data.Copyright, Angela D’Auria Stanton, Ph.D., 2007. All Rights Reserved. Page 4 A Review of Descriptive Statistics Shape of the Distribution The shape of a distribution can be inspected by displaying it graphically. That’s often useful but it can take substantial time, effort and space to produce the graphs. Additionally, graphs cannot be manipulated statistically. Because of this, two coefficients are typically used which indicate the degree and direction of the directions of interval and ratio data with large numbers of values that deviate from a normal distribution. They are: • Skewness of the Distribution o Skewness of a distribution is the degree and direction of its asymmetry. o If a distribution is symmetrical, such as the normal curve, one side of the distribution is precisely the “mirror-image” of the other and the coefficient of skewness will be zero. o


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