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Definition: Used to compare the mean of a sample to a known number (often 0).

Assumptions: Subjects are randomly drawn from a population and the distribution of the mean being tested is normal.

Test: The hypotheses for a single sample t-test are:

H_o: u = u₀

H_a: u < > u₀

(where u₀ denotes the hypothesized value to which you are comparing a population mean)

Test statistic: The test statistic, t, has N-1 degrees of freedom, where N is the number of observations.

Results of the t-test: If the p-value associated with the t-test is small (usually set at p < 0.05), there is evidence to reject the null hypothesis in favor of the alternative. In other words, there is evidence that the mean is significantly different than the hypothesized value. If the p-value associated with the t-test is not small (p > 0.05), there is not enough evidence to reject the null hypothesis, and you conclude that there is evidence that the mean is not different from the hypothesized value.

Example: Single Sample t-test

You read in an article that an educator claimed that the average educational level for people over 60 in was 8th grade. You happen to have a data (ELDERLY.DBF) that contains a random sample of elderly people, and you want to test the educator's claim. The results of performing a single sample t-test are:

   -------------------------------------------------------------------

   Single Sample t-test                              

   -------------------------------------------------------------------

   Variable Name is EDUC

 

   N         =    166                Missing or Deleted = 0

   Mean      = 10.07831                   St. Dev (n-1) = 3.25109

 

   Null Hypothesis: mean(POPULATION) =  8

 

   Calculated t = 8.24 with 165 D.F.   p =  < 0.001  (2 - sided test)

 

   95% C.I. about Mean is (9.57995, 10.57667)

 

   A low value of p supports rejection of the null hypothesis.

   There is evidence that the actual mean is different from the

   hypothesized mean.

Exercise - Single Sample t-test

You have been told that the average employee for your industry has an average dexterity score of 100 on a standardized test. You think your employees will score differently, so you give a random sample of 12 the test. The results are:

Subj. Test Score
1     98
2     102
3     120
4     140
5     123
6     101
7     89
8     99
9     119
10    103
11    132
12    107
 

1. Perform a single sample t-test on this data.

2. What are your hypotheses?

3. What conclusion do you make?

4. Use the Detailed Statistics option to calculate a 95% confidence interval on the mean. How does this approach differ from doing the t-test?

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"Winks is an excellent basic program that runs well on my laptop.  I find that I use it more than SAS"  - Dr. Jim Dickson, Iowa State University

• Statistical Software designed for your needs -- Medical, Clinical Trials, Dissertation, Thesis, Business, Marketing, Agriculture, Forestry, Science and Research.

• WINKS is an economical, reliable and simple to use statistical analysis tool designed to help students and researchers get the statistical answers they need quickly and without hassle.

• It contains a wide range of statistical tests including many handy features not found in programs such as SPSS or SAS -- for example, easy analysis from summary data (as well as from raw data), nonparametric multiple comparisons, APA standard analysis write-up suggestions and more.

• Newest additions to WINKS (ver 6.05) includes Grubbs Test for outliers  and Tukey Test for outliers, Kwikstat Data Generator evaluation edition, multiple comparisons in 2xc and rx2 crosstabulation (Chi-Square) analysis)  & Permutations and combinations calculator

• Statistical test such as t-tests (paired t test, independent group t test/unpaired t test), ANOVA, regression, correlation, repeated measures, logistic regression, times series analysis, chi-square, Bland-Altman, Kruskal-Wallis, Mann-Whitney and much more.

• Friendly interface with easy Excel-like data handling & graphs (reads and writes Excel files.)

• FAST delivery to you when you order now

• Print a brochure (pdf format)

• Recent updates include

  • Added ability to calculate new column of z-scores for numeric variables.
  • Increased maximum groups to 40 for one-way ANOVA and one-way repeated measures (40 repeats).
  • Added editor option to create indicator variables from categorical variables.
  • Added Outcomes and Probabilities module that calculates combinations and permutations.
  • Added Grubbs & Tukey tests for outliers.
  • Added Multiple Comparisons of Proportions to Crosstabulations procedures for 2xc or rx2 tables
  • Updates are free to current users.

Read more about WINKS features.

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For more information... we recommend:

• WINKS -- a simple to use and affordable statistical software program that will help you analyze, interpret and write-up your results. Download a free trial copy.
   

• Additional statistics tutorials.
   

• Against All Odds VIDEOS - Now in VHS or DVD formats Teaching Videos from Annenberg/PBS Click here for info
   

• BeSmartNotes Reference sheets for SAS, SAS ODS, SPSS and WINKS  - Click here for info. (www.besmartnotes.com)
   

• Statistical Analysis Quick Reference Guidebook: With SPSS Examples is a practical "cut to the chase" handbook that quickly explains the when, where, and how of statistical data analysis as it is used for real-world decision-making in a wide variety of disciplines. It contains examples using SPSS Statistics software. In this one-stop reference, the authors  provide succinct guidelines for performing an analysis, avoiding pitfalls, interpreting results, and reporting outcomes. Paperback. Sage Publishers ISBN: 1412925606 Order book from Amazon

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