﻿ One-Way Analysis of Variance

# One-Way Analysis of Variance

### Statistics > ANOVA > One-Way

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.

### Dialog box items

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.

### Data

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.

### Charts

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.

### Options

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%.

### Example

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

### Interpreting the results

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).