Z Score Excel Data Analysis

[Barton Ostby]

Thedata analysis functions can be used on only one worksheet at a time. When you perform data analysis on grouped worksheets, results will appear on the first worksheet and empty formatted tables will appear on the remaining worksheets. To perform data analysis on the remainder of the worksheets, recalculate the analysis tool for each worksheet.

The Analysis ToolPak includes the tools described in the following sections. To access these tools, click Data Analysis in the Analysis group on the Data tab. If the Data Analysis command is not available, you need to load the Analysis ToolPak add-in program.

The Anova analysis tools provide different types of variance analysis. The tool that you should use depends on the number of factors and the number of samples that you have from the populations that you want to test.

This tool performs a simple analysis of variance on data for two or more samples. The analysis provides a test of the hypothesis that each sample is drawn from the same underlying probability distribution against the alternative hypothesis that underlying probability distributions are not the same for all samples. If there are only two samples, you can use the worksheet function T.TEST. With more than two samples, there is no convenient generalization of T.TEST, and the Single Factor Anova model can be called upon instead.

This analysis tool is useful when data can be classified along two different dimensions. For example, in an experiment to measure the height of plants, the plants may be given different brands of fertilizer (for example, A, B, C) and might also be kept at different temperatures (for example, low, high). For each of the six possible pairs of fertilizer, temperature, we have an equal number of observations of plant height. Using this Anova tool, we can test:

Whether having accounted for the effects of differences between fertilizer brands found in the first bulleted point and differences in temperatures found in the second bulleted point, the six samples representing all pairs of fertilizer, temperature values are drawn from the same population. The alternative hypothesis is that there are effects due to specific fertilizer, temperature pairs over and above the differences that are based on fertilizer alone or on temperature alone.

This analysis tool is useful when data is classified on two different dimensions as in the Two-Factor case With Replication. However, for this tool it is assumed that there is only a single observation for each pair (for example, each fertilizer, temperature pair in the preceding example).

The CORREL and PEARSON worksheet functions both calculate the correlation coefficient between two measurement variables when measurements on each variable are observed for each of N subjects. (Any missing observation for any subject causes that subject to be ignored in the analysis.) The Correlation analysis tool is particularly useful when there are more than two measurement variables for each of N subjects. It provides an output table, a correlation matrix, that shows the value of CORREL (or PEARSON) applied to each possible pair of measurement variables.

The correlation coefficient, like the covariance, is a measure of the extent to which two measurement variables "vary together." Unlike the covariance, the correlation coefficient is scaled so that its value is independent of the units in which the two measurement variables are expressed. (For example, if the two measurement variables are weight and height, the value of the correlation coefficient is unchanged if weight is converted from pounds to kilograms.) The value of any correlation coefficient must be between -1 and +1 inclusive.

The Correlation and Covariance tools can both be used in the same setting, when you have N different measurement variables observed on a set of individuals. The Correlation and Covariance tools each give an output table, a matrix, that shows the correlation coefficient or covariance, respectively, between each pair of measurement variables. The difference is that correlation coefficients are scaled to lie between -1 and +1 inclusive. Corresponding covariances are not scaled. Both the correlation coefficient and the covariance are measures of the extent to which two variables "vary together."

The Covariance tool computes the value of the worksheet function COVARIANCE.P for each pair of measurement variables. (Direct use of COVARIANCE.P rather than the Covariance tool is a reasonable alternative when there are only two measurement variables, that is, N=2.) The entry on the diagonal of the Covariance tool's output table in row i, column i is the covariance of the i-th measurement variable with itself. This is just the population variance for that variable, as calculated by the worksheet function VAR.P.

The Exponential Smoothing analysis tool predicts a value that is based on the forecast for the prior period, adjusted for the error in that prior forecast. The tool uses the smoothing constant a, the magnitude of which determines how strongly the forecasts respond to errors in the prior forecast.

For example, you can use the F-Test tool on samples of times in a swim meet for each of two teams. The tool provides the result of a test of the null hypothesis that these two samples come from distributions with equal variances, against the alternative that the variances are not equal in the underlying distributions.

The Fourier Analysis tool solves problems in linear systems and analyzes periodic data by using the Fast Fourier Transform (FFT) method to transform data. This tool also supports inverse transformations, in which the inverse of transformed data returns the original data.

For example, in a class of 20 students, you can determine the distribution of scores in letter-grade categories. A histogram table presents the letter-grade boundaries and the number of scores between the lowest bound and the current bound. The single most-frequent score is the mode of the data.

The Moving Average analysis tool projects values in the forecast period, based on the average value of the variable over a specific number of preceding periods. A moving average provides trend information that a simple average of all historical data would mask. Use this tool to forecast sales, inventory, or other trends. Each forecast value is based on the following formula.

The Random Number Generation analysis tool fills a range with independent random numbers that are drawn from one of several distributions. You can characterize the subjects in a population with a probability distribution. For example, you can use a normal distribution to characterize the population of individuals' heights, or you can use a Bernoulli distribution of two possible outcomes to characterize the population of coin-flip results.

The Rank and Percentile analysis tool produces a table that contains the ordinal and percentage rank of each value in a data set. You can analyze the relative standing of values in a data set. This tool uses the worksheet functions RANK.EQ andPERCENTRANK.INC. If you want to account for tied values, use the RANK.EQ function, which treats tied values as having the same rank, or use the RANK.AVG function, which returns the average rank for the tied values.

The Regression analysis tool performs linear regression analysis by using the "least squares" method to fit a line through a set of observations. You can analyze how a single dependent variable is affected by the values of one or more independent variables. For example, you can analyze how an athlete's performance is affected by such factors as age, height, and weight. You can apportion shares in the performance measure to each of these three factors, based on a set of performance data, and then use the results to predict the performance of a new, untested athlete.

The Sampling analysis tool creates a sample from a population by treating the input range as a population. When the population is too large to process or chart, you can use a representative sample. You can also create a sample that contains only the values from a particular part of a cycle if you believe that the input data is periodic. For example, if the input range contains quarterly sales figures, sampling with a periodic rate of four places the values from the same quarter in the output range.

The Two-Sample t-Test analysis tools test for equality of the population means that underlie each sample. The three tools employ different assumptions: that the population variances are equal, that the population variances are not equal, and that the two samples represent before-treatment and after-treatment observations on the same subjects.

For all three tools below, a t-Statistic value, t, is computed and shown as "t Stat" in the output tables. Depending on the data, this value, t, can be negative or nonnegative. Under the assumption of equal underlying population means, if t This analysis tool performs a two-sample student's t-Test. This t-Test form assumes that the two data sets came from distributions with the same variances. It is referred to as a homoscedastic t-Test. You can use this t-Test to determine whether the two samples are likely to have come from distributions with equal population means.

This analysis tool performs a two-sample student's t-Test. This t-Test form assumes that the two data sets came from distributions with unequal variances. It is referred to as a heteroscedastic t-Test. As with the preceding Equal Variances case, you can use this t-Test to determine whether the two samples are likely to have come from distributions with equal population means. Use this test when there are distinct subjects in the two samples. Use the Paired test, described in the follow example, when there is a single set of subjects and the two samples represent measurements for each subject before and after a treatment.

The following formula is used to calculate the degrees of freedom, df. Because the result of the calculation is usually not an integer, the value of df is rounded to the nearest integer to obtain a critical value from the t table. The Excel worksheet function T.TEST uses the calculated df value without rounding, because it is possible to compute a value for T.TEST with a noninteger df. Because of these different approaches to determining the degrees of freedom, the results of T.TEST and this t-Test tool will differ in the Unequal Variances case.

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