for confidence intervals and hypothesis tests

- SE for a single mean: No calculator is provided
here.

Use the sample standard deviation divided by the square root of the sample size.

Use the summary statistic calculator with the sample data to find the sample standard deviation. http://visualize.tlok.org/intro-stat/statistic.php

- SE for difference of means of paired data

For each pair, compute the difference. Consider the collection of these differences as the data. Analyze it as data on one sample mean.

- SE for the difference of sample means from independent samples
SE sample means

If necessary, use the summary statistic calculator with each set of sample data to find its sample standard deviation. http://visualize.tlok.org/intro-stat/statistic.php

This SE calculator also gives the accurate value for the degrees of freedom. Round to the nearest whole number to use a t-table to find probabilities in the appropriate t-distribution.

- SE for a single proportion SE one sample proportion

- SE for the difference of sample proportions SE sample proportions

- Difference of two sample means from two independent
samples:
http://visualize.tlok.org/intro-stat/standard_error_diff_two_sample_means.php

- One proportion: http://visualize.tlok.org/intro-stat/standard_error_one_sample_proportion.php
- Difference of two sample proportions from independent
samples:
http://visualize.tlok.org/intro-stat/standard_error_diff_two_sample_proportions.php

See calculators for theoretical sampling distributions

**ANOVA for Difference of Means**

StatKey will produce full results in an ANOVA tablewhen given the full dataset with the values. It will not produce an ANOVA table for data for which you only have summaries. (Presumably that's because you really need the full datasets to have the comparative graphs you would like to see first.) This applet produces an ANOVA table, from which you can find the F-statistic and p-value, from summarized data. http://www.tlok.org/visualize/intro-stat/anova_difference_of_means.php

With example http://www.tlok.org/visualize/intro-stat/anova_difference_of_means.php?file=anova_example.txt

This applet http://visualize.tlok.org/intro-stat/regression_intervals.php calculates the CI (confidence interval for the mean y for a given x-value) and the PI (prediction interval for a single y for a given x-value)

The interval is at the lower right of the
screen. There
are two different types of intervals, **so you must choose one of
the types of intervals with one of the green buttons.
After you obtain that, you may choose the other. **

Follow these steps to produce it yourself. (Not required in this
course.)

- ·
Copy and paste the data
into the textbox at the
top left.
- ·
Enter your chosen x-value
below that.
- ·
Choose which type of
interval you want in the
lower left.