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One-way ANOVA

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QXL Stat Tools Tab > Hypothesis Tests > Tests for Mean > One-way ANOVA

Test type: Mean
Data: Quantitative
Number of Variables: 1
Number of Groups: 2 or more
Assumptions: Normally distributed samples with equal variance

One-way ANOVA is a hypothesis test used to compare the means of two or more samples. The null hypothesis is that there is no difference in the population means.

You can use a One-way ANOVA when the following conditions are met:

  • Samples are independent.

  • Populations are normally distributed.

  • Population variances are equal.

If the data is not normally distributed, use Mood's Median or Kruskal-Wallis instead.

Hypothesis tested:

H0 : μ1 = μ2 = ... = μn
H1 : μi ≠ μj

where μk is the population mean.

Step #1: Select data source for one-way ANOVA.

Data for the one-way ANOVA can come from an Excel spreadsheet, SQL data source, or it can be entered manually.

See source data formats and example data for the one-way ANOVA.

Step #2: Options.

  • 'Decision Criteria' option (default = 0.05). The value of the decision criteria (significance or α level).

  • 'Show Box plot' option. Display box plot along with hypothesis results.

  • 'Display mode' option. When the 'Verbose (long)' option is on, Quantum XL will display additional text that explains the hypothesis test results.

Example

We have measured the time it takes to load the same web page from three different geographic locations. Our interest was to check if there is a difference between average load time of those locations.

One-Way ANOVA results

Quantum XL will display the ANOVA table and 95% confidence intervals for the mean.

From the ANOVA table we can see that p Value= 0.059. Since it is greater than the decision criteria (0.05) the null hypothesis cannot be rejected. We do not have enough evidence to say that means are different.

Update

One-way ANOVA is updatable. After you create a one-way ANOVA analysis, you can change its data source or add new data to the data source and simply update the analysis.

  • Update: Quantum XL > Statistical Tools > Update Sheet

  • Change settings: Quantum XL > Statistical Tools > Modify Chart/Analysis