normal probability plot

(noun)

a graphical technique used to assess whether or not a data set is approximately normally distributed

Related Terms

Examples of normal probability plot in the following topics:

  • Constructing a normal probability plot (special topic)

    • We construct a normal probability plot for the heights of a sample of 100 men as follows:
    • If the observations are normally distributed, then their Z scores will approximately correspond to their percentiles and thus to the zi in Table 3.16.
    • Because of the complexity of these calculations, normal probability plots are generally created using statistical software.
    • Construction details for a normal probability plot of 100 men's heights.
    • To create the plot based on this table, plot each pair of points, (zi,xi).

  • Normal probability plot

    • We outline the construction of the normal probability plot in Section 3.2.2
    • The histogram shows more normality and the normal probability plot shows a better fit.
    • We first create a histogram and normal probability plot of the NBA player heights.
    • A histogram and normal probability plot of these data are shown in Figure 3.13.
    • A histogram of poker data with the best fitting normal plot and a normal probability plot.

  • Conclusion

    • The above example of a probability histogram is an example of one that is normal.
    • There is another method, however, than can help: a normal probability plot.
    • A normal probability plot is a graphical technique for normality testing--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 form an approximate straight line .
    • Explain how a probability histogram is used to normality of data

  • Probability Histograms and the Normal Curve

    • How can we tell if data in a probability histogram are normal, or at least approximately normal?
    • There is another method, however, than can help: a normal probability plot.
    • A normal probability plot is a graphical technique for normality testing--assessing whether or not a data set is approximately normally distributed.
    • This is a sample of size 50 from a right-skewed distribution, plotted as a normal probability plot.
    • This is a sample of size 50 from a normal distribution, plotted as a normal probability plot.

  • Graphical diagnostics for an ANOVA analysis

    • As with one- and two-sample testing for means, the normality assumption is especially important when the sample size is quite small.
    • The normal probability plots for each group of the MLB data are shown in Figure 5.31; there is some deviation from normality for infielders, but this isn't a substantial concern since there are about 150 observations in that group and the outliers are not extreme.
    • Then to check the normality condition, create a normal probability plot using all the residuals simultaneously.
    • This assumption can be checked by examining a side- by-side box plot of the outcomes across the groups, as in Figure 5.28 on page 239.
    • The normality condition is very important when the sample sizes for each group are relatively small.

  • Introduction to evaluating the normal approximation

    • Many processes can be well approximated by the normal distribution.
    • While using a normal model can be extremely convenient and helpful, it is important to remember normality is always an approximation.
    • Testing the appropriateness of the normal assumption is a key step in many data analyses.
    • The observations are rounded to the nearest whole inch, explaining why the points appear to jump in increments in the normal probability plot.

  • A sampling distribution for the mean

    • Now we'll take 100,000 samples, calculate the mean of each, and plot them in a histogram to get an especially accurate depiction of the sampling distribution.
    • The distribution of sample means closely resembles the normal distribution (see Section 3.1).
    • A normal probability plot of these sample means is shown in the right panel of Figure 4.9.
    • Under the normal model, we can make this more accurate by using 1.96 in place of 2.
    • The right panel shows a normal probability plot of those sample means.

  • Checking model assumptions using graphs

    • A normal probability plot of the residuals is shown in Figure 8.9.
    • In a normal probability plot for residuals, we tend to be most worried about residuals that appear to be outliers, since these indicate long tails in the distribution of residuals.
    • These plots are shown in Figure 8.12.
    • There appears to be curvature in the residuals, indicating the relationship is probably not linear.
    • A normal probability plot of the residuals is helpful in identifying observations that might be outliers.

  • Homogeneity and Heterogeneity

    • Imagine that you have a scatter plot, on top of which you draw a narrow vertical strip.
    • To the extent that the histogram matches the normal distribution, the residuals are normally distributed.
    • When various vertical strips drawn on a scatter plot, and their corresponding data sets, show a similar pattern of spread, the plot can be said to be homoscedastic.
    • Consequently, each probability distribution for $y$ (response variable) has the same standard deviation regardless of the $x$-value (predictor).
    • To the extent that a residual histogram matches the normal distribution, the residuals are normally distributed.

  • Quantile-Quantile (q-q) Plots

    • That is, the probability a normal sample is less than ξq is in fact just q.
    • As before, a normal q-q plot can indicate departures from normality.
    • The q-q plots may be thought of as being "probability graph paper" that makes a plot of the ordered data values into a straight line.
    • Every density has its own special probability graph paper.
    • Figure 12. q-q plots for standardized non-normal data (n = 1000)