Quantitative - One Population The Quantitative One Population VISA procedures allow the user to perform descriptive and inferential procedures for problems involving one population with quantitative (interval) data. Data is entered for up to 1000 observations in worksheet ED. Three analytical sections are provided: Descriptive (graphical and numerical) Analysis Procedures Inferential Analysis Procedures Calculate Sample Size The worksheets for these procedures are: SG shows a scatter plot of the data as entered DP shows a dot plot of the data by data value. The dot plot graph displays the maximum, minimum, mean and median values. It also shows bands for data within 1, 2 and 3 standard deviations of the mean BW shows the box plot and dot plot on the same graph. It identifies the minimum and maximum whisker values along with the first quartile, median, and third quartile boxes. This presentation allows the user visualize skew and identify outliers which can be deleted from the ED worksheet. HIST allows the user to visualize a histogram of the data. A radio button option allows the user to view the histogram by a specific bins classification or one that is generated automatically by Sturge s formula NDS provides the numerical descriptive statistics for central tendency (mean, median, mode, quartiles and percentiles), variation (variance, standard deviation, maximum, minimum, range, inter-quartile range, and coefficient of variation) and skew. The count and sum of the data observations are also shown COMP allows the user to visualize a histogram of the data compared to the expected normal distribution. If the observations are at least 32, the user can select a significance level to automatically observe the Rule of 5 Chi-Square test results for normality PE provides point estimates for the population mean, standard deviation and variance CI based on a user selected confidence level, the population Confidence Interval is calculated for the parameters: mean, variance and standard deviation HT allow the user to select a radio button for the known variation (Z) or unknown variation (t) Hypothesis Test. The user enters a significance level, hypothesized value and chooses from a option box for a two tail (not equal), right tail (greater than) or left tail (less than) test. The p-value is displayed with an interpretation of the results SS - calculates the Sample Size necessary for a user selected allowable error and confidence level Example: In this example a sports marketing manager is evaluating the attendance at baseball games where there are no promotional giveaways (e.g. souvenir balls). In this example the data does not appear to be skewed and no outliers are present. However, if there are outliers, the user can mouse over the point and identify its value. If the user determines any outliers should be eliminated they can return to the ED worksheet and eliminate it from the original input. If any outliers are identified and deleted, the data must be resorted.
PROCEDURES worksheet ED worksheet Click the Sort Data before returning macro after entering the data. Outliers are automatically identified. 2
SG worksheet Displays a scatter gram of the data in observational sequence it was entered. DP worksheet Displays a dot plot of the data with numerical descriptive information Minimum Maximum Mean 3
Median +/- 1 standard deviation +/- 2 standard deviations +/- 3 standard deviations BW worksheet Displays the box & whisker plot The student can immediately see the central location, spread, shape and make any outlier identification. Mouse over any point to see the data value for the point. In this example, the outliers have been eliminated from the data. 4
HIST worksheet This worksheet displays information necessary for the user to evaluate a histogram of the data (# Observations, Minimum Value, Maximum Value and Range). User selected classifications The user has an option to view a histogram by selecting a radio button for one of the following: Equal class using Sturges Formula Scrolling down HIST worksheet (continued) In this example, Sturges classifications are shown. 5
NDS worksheet The numerical descriptive statistics are displayed. An entry can be made to investigate percentile calculations. If there are less than 32 observations, the user can view the data for an extremely non-normal situation. COMP worksheet. A graph of the observed data (red) and expected normal distribution (pink) are shown allowing the user to evaluate the normality requirement for the confidence interval and hypothesis tests. If there are at least 32 observations the user can enter a significance level (cell F8) to observe the Chi- Square (rule-offive) test for Normality results. 6
PE worksheet This worksheet displays the point estimates for the population parameters (mean, standard deviation, and variance) based on the sample. CI worksheet This allows the user to select a radio button for: Known variation Unknown variation If the variation is known the user is required to enter the value. If it is unknown, the degrees of freedom (df) are automatically displayed. Scrolling down 7
CI worksheet (continued) Once the confidence level is entered, the confidence intervals are displayed for the following population parameters: Mean Standard Deviation Variance A verbal explanation of the confidence interval is also provided. HT worksheet Similar to the CI worksheet the user can select a radio button option for known or unknown variation. When the significance level, hypothesized value, and alternative option box selection is made, the results along with a verbal explanation are shown. In this example, if we are testing: Is non-promotional attendance greater than 15,000? The hypothesis test p-value is 1.0000 which implies the null hypothesis is statistically true. This information allows the user to develop a conclusion in non-statistical, easy to understand terminology. 8
SS worksheet 9