The t-statistic
Serves as an alternate to a z-score
z-score requires much more information than t-score
When standard deviation (variance) is unknown for a population, use the sample value in its place.
Degrees of Freedom: describes number of scores in a sample that are independent and free to vary.
Estimated standard error is used as an estimate of the real standard error.
Provides estimate of the standard difference between a sample mean and the sample population.
Shifts from standard deviation to variance for two reasons: 1. the sample variance is an unbiased statistic. 2. to maximize similarity from one version to another.
Formula: 
Uses estimated standard error in the denominator
As sample size increases, the better the sample variance represents the population variance. Similar to law of large numbers.
The t-distribution: compute t-statistic for each sample value and the entire set will form a t-distribution.
The t-distribution approximates the shape of a normal disribution
Bell shaped, symmetrical, and have a mean of 0.
Flatter and more spread out than pointed z-score distribution.
Different shape than z-score distribution as a result of the variance in bottom of t-score formula.
T-distribution table used to find proportion for statistics.
The numbers in the table indicate the values of t that separate the tails from the main body of the distribution.
Total of 10% found in two combined tails.
Hypothesis Testing: use a sample from the treated population as a basis to determine if the treatment has any effect.
Null hypothesis states that the treatment has no effect.
Provides a specific value for the unknown population mean.
Creates a ratio
Can be obtained from a theory, logical prediction, or wishful thinking.
Basic Assumptions are for hypothesis tests with t-statistics.
- The values in the sample must consist of independent observations.
The sampled population must be normal
Sample Size and Sample Variance:
Sample variance is related to estimated standard error in that the larger the variance, the larger the error.
Estimated standard error is inversely related to the number of scores in the sample. The larger the sample, the smaller the error.
Measures of Effect:
Population values are not known and are replaced by sample values.
Referred to as "estimated d."
Formula:
Alternate method is to determine how much variability in the scores is explained by the treatment effect.
Accomplished through measuring difference before and after removal of treatment effect.
Confidence intervals: alternative technique for describing treatment effect. Accomplished by computing an estimate of the population mean after treatment.
Should be relatively near to the corresponding population parameter.
Interval or range of values centered around a sample statistic.
Formula for confidence interval:
Wider interval= more confidence; narrower interval= less confidence
The larger the sample, the more narrow the interval.
Directional Hypothesis and One-Tailed Test:
One tailed test may be used when a previous theory exists.
If test statistic is found to be in critical region, then the null hypothesis is rejected.
Determine if sample mean is in direction predicted by the original research question.
Determine if effect is large enough to be significant.