Time Series Plot and One-Way ANOVACan You Count On Weather Forecasts?

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    Time Series Plot and One-Way ANOVA

    Can You Count On Weather Forecasts?

    People consult weather forecasts to determine their activities, what to wear, or what to pack for a trip. But are these predictions trustworthy, or just a lot of hot air?

    You can use the Assistant in Minitab Statistical Software to find out.

    Try It Yourself

    The data set collects 30 days’ worth of next-day, 5-day, and 10-day high temperature forecasts (in degrees F) for State College, Pennsylvania—the home of Minitab’s World Headquarters. The data sheet also includes the actual high temperature for each day, and the differences between the forecasted and actual high temperatures.

    Step 1: See the Data

    Graphing your data is always a good first step. Select Assistant > Graphical Analysis… for guidance on what graphs might offer insight about this data.

    The Assistant presents three objectives to choose from.


    You’re investigating how closely the forecasts match the real high temperature. These data were recorded in the order they occurred, so graphing the variables over time could be useful. Select “Time Series Plot.”

    Since each type of forecast is in its own column, select “Y data are in more than one column.” Then enter the columns for each of the three forecasts as well as the one that lists the actual temperature.

    Click OK and Minitab produces a Report Card that addresses assumptions for this analysis, a Diagnostic Report that helps identify patterns in the data, and the following Summary Report:

    If the forecasts were consistent with the actual high temperatures, the four lines on the time series plot would stick close together as they run from left to right. They don’t. Sometimes the points are close, but frequently they veer sharply away from one another. The blue line representing the 10-day forecasts often seems particularly distant from the purple line representing the actual high. The next-day forecast appears to follow the actual high temperature most closely.

    Step 2: Test the Hypothesis

    The time series plot suggests that the next day, 5-day and 10-day forecasts are not equally reliable. To compare the three forecasts and see if the data support this hypothesis, use Assistant > Hypothesis Tests...

    If you’re not sure which test to use to analyze the data, let the Assistant guide you to the right choice.

    Since these data represent three types of forecasts, you want to compare more than two samples.

    If you select “Help Me Choose”, you can follow the decision tree to the right choice. Since this temperature data is continuous, and you need to compare more than two samples, the decision tree guides you to the One-Way ANOVA.

    Fill out the dialog for One-Way ANOVA as shown, and click OK:

    The Assistant’s Summary Report clearly states that “Differences among the means are significant (p < 0.05).” The Mean Comparisons Chart shows that the 10-day forecast provides a significantly worse weather prediction than the next day forecast, while the 5-day and next-day forecasts appear to be equally accurate.

    The Assistant also produces a Report Card, which checks your data against the assumptions of the analysis and alerts you to any potential issues, so you can be sure your results are reliable.

    The Report Card has flagged one data point as being unusual. However, a review of this data point shows that it is accurate, so it should remain in the analysis. The Report Card also confirms that the sample size is sufficiently large to detect differences and to satisfy assumptions of normality.

    You’ve Weathered this Analysis!

    Your analysis has demonstrated that if you’re going to depend on weather reports to decide what to wear, the next-day forecast or even the 5-day forecast are the most reliable options.

    Of course, weather is a highly variable, extremely complex process—and this data covers only 30 days in one location. Would the results be the same for 30 days of predictions for your part of the world? Now you know how to use the Assistant to find out!

    What else could you discover by using the Assistant to analyze your data?

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