Stats I Final Pitt

When the population variance of a variable is unknown.

It changes the distribution of the test statistic. It is no longer a z-distributed but t-distributed.

When df is small, there is a large difference between the t- and z- distribution. However, when df is large (i.e. greater than 30), there is no noticeable difference.

t-critical will always be bigger than z-critical

amount of difference in SD

Inferential process of using statistics to estimate parameters.

• a single number is used to estimate a parameter
• -null hypothesis testing

a range of values is used to estimate a parameter

• when an interval estimate is accompanied by a specific level of confidence (probability)
• can be computed for any statistic 

• affected by confidence level and standard deviation of a statistic
• - confidence level increases, width of confidence interval increases
• -standard deviation of a statistic increases, width of confidence interval increases

used to compare a mean of the DV between two groups

• df = (n1 -1) + (n2 - 1)
•     = N-2

weighted average of a variances of a DV for group 1 and 2

• Normality
• No Outliers
• Homogeneity of Variance
• Independence of Subjects
• If violated results/conclusion of t-test could be invalid

• DV should be normally distributed within each group
• -tested using the Shapiro-Wilk

• an outlier has an undue influence on a statistic
• assumption is checked by examining histogram and Q-Q plot

the variances of the dependent variable are between group 1 and 2, Leven's test of homogeneity of variance will be used to test this assumption

• design consideration. one subject outcome is not influenced by another's outcome
• not testable

• Non-parametric test
• Alternative to the independent-samples t-test 
• does NOT assume normality 

• changes df to reflect violation of homogeniety
• more violated the smaller the df
• less powerful than t-test