The test and confidence interval depend on the assumption of Normality of the differences. The options button will allow you to construct a confidence interval for the average difference. Assume for the moment that this assumption is valid and carry out a t-test of the hypothesis that the average difference is zero: this can be done using the Stat->Basic Statistics->1 Sample t sequence of menu options. Column three now contains the set of differences, which we assume are random drawing from a Normal distribution. Type the rubber data into c1 and c2 and let c3 = c2 - c1 in the session window. Repeat the whole procedure now for small sample sizes. Draw a histogram, boxplot and dotplot of c2.
To see what kind of probability plots can be expected from skewed data generate 100 data points from a Normal Distribution into c1, then let c2 equal c1 squared: to do this, select Edit->Command Line Editor and type let c2 = c1 * c1. Repeat this whole process a few times to see the kind of variability that can be expected from Normal Probability plots based on samples of 100. Use Scatterplot from the Graphs menu to obtain a Normal probability plot. This calculates Normal scores for the data, which are then used to obtain Normal probability plots. Select Edit->Command Line Editor and type in the command nscores c1 c2. Examine the data you have generated using a Histogram, a Dotplot and a Boxplot and obtain summary statistics ( Stat->Basic Statistics ->Descriptive Statistics). Open Minitab and use Calc->Random Data->Normal to generate 100 observations from a Normal Distribution with mean (\(\mu \) = 0) and standard deviation (\(\sigma \) = 1). We will first explore Normal probability plots using randomly generated data and then use these plots as a means of assessing the assumption of Normality made when we carry out t-tests and construct confidence intervals for process averages, based on small sample sizes.
With fewer points, it becomes harder to distinguish between random variability and a substantive deviation from normality.In this laboratory session, we are going to use Minitab to analyze some experimental data.
Normal plots are often used with as few as 7 points, e.g., with plotting the effects in a saturated model from a 2-level fractional factorial experiment. With more points, random deviations from a line will be less pronounced. If the sample has mean 0, standard deviation 1 then a line through 0 with slope 1 could be used. The further the points vary from this line, the greater the indication of departure from normality. As a reference, a straight line can be fit to the points. If the data are consistent with a sample from a normal distribution, the points should lie close to a straight line. Z i = Φ − 1 ( i − a n + 1 − 2 a ), Īnd Φ −1 is the standard normal quantile function. The formula used by the "qqnorm" function in the basic "stats" package in R (programming language) is as follows: ĭifferent sources use slightly different approximations for rankits.
Some plot the data on the vertical axis others plot the data on the horizontal axis. an approximation to the means or medians of the corresponding order statistics see rankit. The normal probability plot is formed by plotting the sorted data vs.