Which one of the following statements about QQ plots (Normal scores plots) and Normal Probability plots is FALSE?Group of answer choicesA QQ plot is a plot of the inverse cdf for the sample data.With regards to assessing normality, a Normal Probability plot is conceptually the same as a QQ plot - however, the axes are interchanged.A QQ plot is a plot of the sample quantiles against the corresponding quantiles of a standard normal distributionIf a sample is obtained from a Normal population, the QQ plot should be close to a straight line.A Normal Probability plot is a graph of the sample cdf with a (specifically) modified scale on the vertical axis.
Question
Which one of the following statements about QQ plots (Normal scores plots) and Normal Probability plots is FALSE?Group of answer choicesA QQ plot is a plot of the inverse cdf for the sample data.With regards to assessing normality, a Normal Probability plot is conceptually the same as a QQ plot - however, the axes are interchanged.A QQ plot is a plot of the sample quantiles against the corresponding quantiles of a standard normal distributionIf a sample is obtained from a Normal population, the QQ plot should be close to a straight line.A Normal Probability plot is a graph of the sample cdf with a (specifically) modified scale on the vertical axis.
Solution
A QQ plot (quantile-quantile plot) is a plot of the quantiles of two distributions against each other. If the distributions are similar, the points in the QQ plot will approximately lie on the line y = x. If the distributions are linearly related, the points in the QQ plot will approximately lie on a line, but not necessarily on the line y = x.
A Normal Probability plot is a special case of a QQ plot where one of the distributions is a standard normal distribution. It is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.
Given these definitions, let's evaluate each of the options:
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A QQ plot is a plot of the inverse cdf for the sample data. - FALSE. A QQ plot is a plot of the quantiles of two distributions against each other, not the inverse cdf of the sample data.
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With regards to assessing normality, a Normal Probability plot is conceptually the same as a QQ plot - however, the axes are interchanged. - TRUE. Both plots are used to assess normality, and they are conceptually the same except for the interchange of axes.
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A QQ plot is a plot of the sample quantiles against the corresponding quantiles of a standard normal distribution. - TRUE. This is the definition of a QQ plot.
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If a sample is obtained from a Normal population, the QQ plot should be close to a straight line. - TRUE. If the sample is from a normal distribution, the points in the QQ plot will approximately lie on a straight line.
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A Normal Probability plot is a graph of the sample cdf with a (specifically) modified scale on the vertical axis. - TRUE. The Normal Probability plot is a graph of the sample cdf with a modified scale on the vertical axis to match the theoretical normal distribution.
Therefore, the statement "A QQ plot is a plot of the inverse cdf for the sample data." is FALSE.
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