Class OneSampleTTest determines whether a sample from a normal distribution with unknown standard deviation could have a given mean. For example, suppose we wish to determine whether the self-esteem of children from a particular school differ from average, given a known population value of 3.9 on the Rosenberg Self-Esteem Scale. 113 children are tested, with a mean score of 4.0408 and a standard deviation of .6542.
As described Section 6.1, all hypothesis test classes provide two paths for constructing instances of that type: a parameter-based method and a data-based method. Thus, you can construct a OneSampleTTest object by explicitly specifying a sample mean (
), sample standard deviation (
), sample size (
), and population mean (
), like so:
double xbar = 4.0408; double s = .6542; int n = 113; double mu0 = 3.9; OneSampleTTest test = new OneSampleTTest( xbar, s, n, mu0 );
Or by supplying a set of sample data, and the necessary population parameters. For instance, if the sample data is in column 3 of DataFrame df:
double mu0 = 3.9; OneSampleTTest test = new OneSampleTTest( df[3], mu0 );
In this case, the sample mean, standard deviation, and size are calculated from the given data.
In addition to the properties common to all hypothesis test objects (Section 6.1), a OneSampleTTest object provides the following read-only properties:
By default, a OneSampleTTest object performs a two-sided hypothesis test (
) with 
. Non-default test parameters can be specified at the time of construction using constructor overloads, or after construction using the provided Alpha and Type properties, like so:
test.Alpha = 0.05;
Once you've constructed and configured a OneSampleTTest object, you can access the various test results using the provided properties, as described in Section 6.1:
Console.WriteLine( "t-statistic = " + test.Statistic ); Console.WriteLine( "deg of freedom = " + test.DegreesOfFreedom ); Console.WriteLine( "p-value = " + test.P ); Console.WriteLine( "reject the null hypothesis? " + test.Reject);
t-statistic = 2.28786996397591 deg of freedom = 112 p-value = 0.0240223660991041 reject the null hypothesis? True
This indicates that we can reject the null hypotheses (
). We can conclude that the children have self-esteem scores significantly different than average.
Finally, remember that the ToString() method returns a formatted string representation of the complete test results:
One Sample t Test ----------------- Sample mean = 4.0408 Sample standard deviation = 0.6542 Sample size = 113 Population mean = 3.9 Computed t statistic: 2.28786996397591, df = 112 Hypothesis type: two-sided Null hypothesis: sample mean = population mean Alt hypothesis: sample mean != population mean P-value: 0.0240223660991041 REJECT the null hypothesis for alpha = 0.05 0.95 confidence interval: 3.91886249658971 4.16273750341029
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