Random Number Generator

Use the Random Number Generator to create a list of random numbers, based on your specifications. For help in using the Random Number Generator, read the Frequently-Asked Questions or review the Sample Problems.

The numbers generated can be found in the Random Number Table.

Instructions: To find the answer to a frequently-asked question, simply click on the question.

• What are random numbers?
• What is a random number generator?
• What is a random number table?
• How "random" is Stat Trek's Random Number Generator?
• How can I control the number of entries in a single random number table?
• What are the minimum and maximum values in a random number table?
• What does it mean to allow duplicate entries in a random number table?
• What is a seed?

What are random numbers?

Random numbers are sets of digits (i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) arranged in random order. Because they are randomly ordered, no individual digit can be predicted from knowledge of any other digit or group of digits.

What is a random number generator?

A random number generator is a process that produces random numbers. Any random process (e.g., a flip of a coin or the toss of a die) can be used to generate random numbers. Stat Trek's Random Number Generator uses a statistical algorithm to produce random numbers.

What is a random number table?

A random number table is a listing of random numbers. Stat Trek's Random Number Generator produces a listing of random numbers, based on the following User specifications:

• The quantity of random numbers desired.
• The maximum and minimum values of random numbers in the table.
• Whether or not duplicate random numbers are permitted.

How "random" is Stat Trek's Random Number Generator?

Although no computer algorithm can produce numbers that are truly random, Stat Trek's Random Number Generator produces numbers that are nearly random. Stat Trek's Random Number Generator can be used for most statistical applications (like randomly assigning subjects to treatments in a statistical experiment). However, it should not be used to generate numbers for cryptography.

How can I control the number of entries in a single random number table?

The value entered in the text box labeled "How many random numbers" controls the quantity of numbers generated for the random number table. Stat Trek's Random Number Generator can create up to 1000 random numbers for a single random number table. If more random numbers are needed, Users can create additional tables.

What are the minimum and maximum values in the Random Number Generator?

The minimum and maximum values set limits on the range of values that might appear in a random number table. The minimum value identifies the smallest number in the range; and the maximum value identifies the largest number. For example, if we set the minimum value equal to 12 and the maximum value equal to 30, the Random Number Generator will produce a table consisting of random arrangements of the numbers in the range of 12 to 30.

What does it mean to allow duplicate entries in a random number table?

Stat Trek's Random Number Generator allows Users to permit or prevent the same number from appearing more than once in the random number table. To permit duplicate entries, set the drop-down box labeled "Allow duplicate entries" equal to True. To prevent duplicate entries, change the setting to False.

Essentially, allowing duplicate entries amounts to sampling with replacement; preventing duplicate entries amounts to sampling without replacement.

What is a seed?

The seed is a number that controls whether the Random Number Generator produces a new set of random numbers or repeats a particular sequence of random numbers. If the text box labeled "Seed" is blank, the Random Number Generator will produce a different set of random numbers each time a random number table is created. On the other hand, if a number is entered in the "Seed" text box, the Random Number Generator will produce a set of random numbers based on the value of the Seed. Each time a random number table is created, the Random Number Generator will produce the same set of random numbers, until the Seed value is changed.

Note: The ability of the seed to repeat a random sequence of numbers assumes that other User specifications (i.e., quantity of random numbers, minimum value, maximum value, whether duplicate values are permitted) are constant across replications. The use of a seed is illustrated in Sample Problem 1.

Warning: The seed capability is provided for Users as a short-term convenience. However, it is not a long-term solution. From time to time, Stat Trek changes the underlying random number algorithm, to more closely approximate true randomization. A newer algorithm will not reproduce random numbers generated by an older algorithm, even with the same seed. Therefore, the safest way to "save" a random number table is to print it out. The algorithm was last changed on 1/7/2012.

1. A university is testing the effectiveness of two different medications. They have 10 volunteers. To conduct the study, researchers randomly assign a number from 1 to 2 to each volunteer. Volunteers who are assigned number 1 get Treatment 1 and volunteers who are assigned number 2 get Treatment 2. To implement this strategy, they input the following settings in the Random Number Generator:
   
   
   • They want to assign a number randomly to each of 10 volunteers, so they need 10 entries in the random number table. Therefore, the researchers enter 10 in the text box labeled "How many random numbers?".
   • Since each volunteer will receive one of two treatments, they set the minimum value equal to 1; and the maximum value equal to 2.
   • Since some volunteers will receive the same treatment, the researchers allow duplicate random numbers in the random number table. Therefore, they set the "Allow duplicate entries" dropdown box equal to "True".
   • And finally, they set the Seed value equal to 345. (The number 345 is not special. They could have used any positive integer.)
   
   Then, they hit the Calculate button. The Random Number Generator produces a Random Number Table consisting of 10 entries, where each entry is the number 1 or 2. The researchers assign the first entry to volunteer number 1, the second entry to volunteer number 2, and so on.
   
   Using this strategy, what treatment did the first volunteer receive? What treatment did the tenth volunteer receive?
   
   Solution:
   
   This problem can be solved by recreating the exact Random Number Table used by the researchers. By inputting all of the same entries (especially the same Seed value) that were used originally, we can recreate the Random Number Table used by the researchers. Therefore, we do the following:
   
   
   • Enter 10 in the text box labeled "How many random numbers?".
   • Set the minimum value equal to 1 and the maximum value equal to 2.
   • Set the "Allow duplicate entries" dropdown box equal to "True".
   • Set the Seed value equal to 345.
   
   Then, we hit the Calculate button. This produces the Random Number Table shown below.
   
   

   Random Numbers
   2 1 2 1 1 2 1 1 2 2

   
   From the table, we can see that the first entry is "2". Therefore, the first volunteer received Treatment 2. And the second entry is "1". Hence, the second volunteer received Treatment 1. And so on.
   
   
2. We would like to survey 500 families from a population of 20,000 families. Each family has been assigned a number from 1 to 20,000. How can we randomly select 500 families for the survey?
   
   Solution:
   
   We input the following settings in the Random Number Generator:
   
   
   • We want to select 500 families. Therefore, we enter 500 in the text box labeled "How many random numbers?".
   • Since each family has been assigned a number from 1 to 20,000, we set the minimum value equal to 1; and the maximum value equal to 20,000.
   • Since we only want to survey each family once, we don't want duplicate random numbers in our random number table. Therefore, we set the "Allow duplicate entries" dropdown box equal to "False".
   
   Then, we hit the Calculate button. The Random Number Generator produces a Random Number Table consisting of 500 unique random numbers between 1 and 20,000. We will survey the families represented by these numbers - a sample of 500 families randomly selected from the population of 20,000 families.