Standard Error calculators

Visualize Applets for Elementary Statistics students

On this page, most links lead directly to applets. If the link leads to discussion instead of an applet, then the text says discussion. Most applets begin with some values in so that you see what the applet does right away. Some of the applets allow you to enter your own data. (By copy and paste mostly, I expect. Don't spend time typing in data here - there are for quick overviews of concepts.)

If an applet is not completely self-explanatory, or if you want something with more depth, click on the Instructions/Discussion link at the bottom of the applet. There are MANY more applets in this collection than are linked to from this top page. You'll have to find those extra applets from the Discussion pages.

This is a work in progress and not all the topics identified have applets or illustrations available now. Your textbook has many illustrations as well, so we felt it was useful to make this Table of Contents address many things that it is helpful to visualize rather than limit it to those for which we have completed applets.

For the material toward the end of this table, we don't have applets yet. However the tables are organized to help you see the similarities between the techniques. For those chapters, much of what you should visualize is the table itself and what it is telling you about how to understand the new material in terms of previous material you have learned.

Basic Practice of Statistics
7th edition


Topics and relationships to visualize

Use these applets on your own data.


  Data and values to use in these applets 



Frequency graphs of one-variable data

  • Watch animations for graphs of one quantitative variable (includes individual value plot, dotplot, histogram, stemplot.)
  • Categorical data (bar graph, pie chart) (graphing applets not yet included, but discussion is included in the next link about in-depth exploration)
  • See more in-depth exploration of all the above 
Chapter 1  

Other graphs of one-variable data

Chapter 2  

Summary statistics of one-variable data

Chapter 2  

Comparative graphs of one-variable data

Chapter 3  

Graphs of population data

Chapter 3 and 20, 21  

Samples from populations

histograms of samples
(You can't enter population data here, but you can choose from three different populations.)
Chapters 4, 5 and 26

Relationships between two quantitative variables

Chapters 6 and 25

Relationships between two (or three) categorical variables

Chapter 9  

Experimental Design

  • Why is random assignment to treatment groups an important part of controlling the effects of outside variables?
Chapter 12  


Probabillity as a long-term relative frequency

(You can't enter data here - you can enter the probability of an event and the simulate MANY occurances of the event to see the pattern of the relative frequency.)

Chapter 15 and 22



Sampling Distributions of various statistics

  • Mean (quantitative variable)
  • Proportion (categorical variable)


Chapter 16 and 20

Chapter 22


Estimation of one parameter (mean or proportion) with confidence intervals

Standard Error calculators (including SE for one proportion)

Put in sample mean, etc.

Chapter 17, 20, and 22



Hypothesis testing of a claim on one variable (mean or proportion)
by finding and interpreting p-values

Standard Error calculators (including SE for one proportion)


Chapters 21 and 23  

Inference on difference of two parameters (means or proportions)

Standard Error calculators  (including SE for one proportion, difference of two means, difference of two proportions)

Matched Pairs.  The statistical method is to find the difference for each pair, and then analyze the set of differences as a one-variable problem.    This applet takes the matched pairs data as input and  finds the entire set of differences and the mean and standard deviation of those differences.   

  means proportions
Sampling distribution t normal
p-value shading in t-dist'n shading in normal dist'n
numerical/graphical summaries compare boxplots compare the two proportions

Chapter 25 and 27.

Extension of ideas from Chapters 23 and 21.


Inference on comparing multiple (two or more) parameters (proportions or means)

  proportions means
Sampling distribution chi-squared (categorical variables)

F (quantitative variable on groups - the group designation is a categorical variable.) 
p-value shading to the right of the data value in a picture in a (skewed) chi-square dist'n
  • Use StatKey to produce the table and compute the test statistic,  chi-square.
Use StatKey theoretical chi-squared  dist'n to find the p-value.
shading to the right of the data value in a picture in a (skewed) F dist'n
  • If you have the full datasets, use StatKey to find the test statistic, F.
  • If you only have summary statistics, use the Visualize Anova applet   to find the test statistic, F.
Use StatKey theoretical F dist'n to find the p-value.
numerical / graphical summaries compare conditional distributions compare boxplots

Chapter 26.

Uses concepts and techniques from Chapters 4 and 5


Inference on relationships between two (or more) quantitative variables (regression)

This table shows what is covered in this chapter.
New material for this chapter:  (You must input quantitative data in two columns.  Data for the Moore textbook.)

Material covered in Chapters 4 and 5

    population y-intercept population standard deviation of points around line population slope coefficient population correlation coefficient Given an x-value, estimate mean of all y-values for it. Given an x-value, estimate an individual y-value
estimate with one number   yes yes yes yes yes yes
estimate with an interval   no no yes no yes yes
hypothesis test   no no yes yes no no
check conditions  
Yes. Conditions must be met for inference on any of these.

Information about entering data for our applets

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