Computes and summarizes a traditional one-way analysis of variance.

This procedure compares the sample means for k groups. Analysis of variance (ANOVA) extends the two-sample t-test, which compares two population means.

•Samples in one column:

Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oResponse: Enter the column containing the response data.

oFactor: Enter the columns containing the factor levels.

•Samples in different columns:

Choose if the data of the two samples are in separate columns.

oSamples: Enter the column containing the samples.

•Report:

The display of outputs of VisualStat.

The response variable must be numeric. Stack the response data in one column with another column of level values identifying the population. The factor column can be numeric, or text. Samples can also be in separate numeric columns.

Displays a histogram, a histogram with a normal curve, and a boxplot.

•Histogram:

Choose to display a histogram for each variable

•Histogram with Normal Curve:

Choose to display a histogram with a normal curve for each variable

•Boxplot of data:

Choose to display a boxplot for each variable

•Options:

Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.

•Estimations:

Check this box to calculate descriptive statistics for each dependent variable for each group, including number of cases, mean, standard deviation, standard error of the mean, effect, minimum, maximum, and confidence intervals.

•Alternative Hypothesis:

Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

•Confidence Level:

Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

Parents are frequently concerned when their child seems slow to begin walking. In 1972, Science reported on an experiment in which the effects of several different treatments on the age at which a child’s first walks were compared. Children in the first group were given special walking exercises for 12 minutes daily beginning at the age 1 week and lasting 7 weeks. The second group of children received daily exercises, but not the walking exercises administered to the first group. The third and forth groups received no special treatment and differed only in that the third group’s progress was checked weekly and the forth was checked only at the end of the study.

1.Open the DataBook anova.vstz

2.Select the sheet WalkingAge

3.Choose the tab Statistics, the group Anova and the command One-Way

4.Select group Samples in one column

5.In Response, select Age (months). In Factor, select (Treatment) Group.

6.Click Options page and check Estimation.

7.Click OK

Report window output

One-Way Analysis of Variance

-=-=-=-= Age (months) / (Treatment) Group =-=-=-=-

ANOVA TABLE

df SumOfSquares Mean Square F P

Between groups 3 14.7778 4.9259 2.1422 0.1285

Within groups 19 43.6896 2.2995

Total 22 58.4674 2.6576

Residual Standard Deviation 1.516394E+000

Residual Degrees of Freedom 22

Grand Mean 1.134783E+001

ESTIMATION

N Mean StDev SE Mean Effect 95% LCL 95% UCL Minimum Maximum

1 6 10.1250 1.4470 0.5907 -1.2228 8.6065 11.6435 9.0000 13.0000

2 6 11.3750 1.8957 0.7739 0.0272 9.3856 13.3644 10.0000 15.0000

3 6 11.7083 1.5200 0.6205 0.3605 10.1132 13.3035 9.0000 13.2500

4 5 12.3500 0.9618 0.4301 1.0022 11.1558 13.5442 11.5000 13.5000

<total> 23 11.3478 1.6302 0.3399 0.0000 10.6429 12.0528 9.0000 15.0000

These data show that a child's true mean walking age is not statistically significantly different among any of the four treatment groups (p = 0.1285).

See Also: |

Two-Sample t Test | Report | Numeric Formats

Web Resource: Weisstein, Eric W., Wolfram MathWorld. | NIST e-Handbook of Statistical Methods, 2006 | Probability and statistics EBook