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Statistics I: Final
University of Guelph STAT*2040
37
Mathematics
Undergraduate 2
04/13/2015

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Cards

Term
ANOVA
Definition
Analysis of variance. Tests the null hypothesis that the population means are all equal by comparing the variability between groups to the variability within groups.
Term
Bootstrap method
Definition
A method of inference for two means.
Term
Coefficient of determination (R2)
Definition

Sample variance of Y hat / Samle variance of Y

The square of the correlation coefficient. The proportion of variance in Y that can be explained by the linear relationship with X. The closer to 1, the stronger the relationship.

Term
Correlation coefficient (r)
Definition

-1 < r < +1

A unitless measure of the strength of the linear relationship between X and Y. The father from zero, the stronger the relationship.

Term
Dependent samples
Definition
Multiple measurements made on the same individual, or linked individuals such as identical twins. Reduces variability. Easier to isolate the effect of interest.
Term
Expected
Definition
The counts we would get on average if the null hypothesis was true. For a test for independence, it is (row total x column total) / overall total.
Term
Explanatory variable (X)
Definition
Independent variable. Used to predict Y.
Term
F statistic
Definition

MST / MSE

Predicts the p-value in an ANOVA test.

Term
Goodness-of-fit test
Definition
A chi-square test for a one-way table. Observations are classified according to one categorical variable.
Term
Homoscedastic
Definition
Has the same variance.
Term
Independent samples
Definition
Use pooled-variance procedure or Welch procedure.
Term
Inference for two means
Definition
Testing if there is a significant difference between the means of two groups, and finding a confidence interval. The difference of the sample means is an unbiased estimator of the difference in population mean. If both have normal distribution, the difference will have normal distribution. Options include pooled-variance t procedure, Welch procedure, Mann-Witney U, bootstrap methods, and permutaiton tests.
Term
Mann-Witney U
Definition
A metho of inference for two means.
Term
Match-pairs
Definition
Individuals that are grouped into pairs according to variables that are likely to affect the response. Treated as single samples.
Term
Method of least squares
Definition
β0 hat and β1 hat are chosen so that the sum of squred residuals is minimized.
Term
MSE
Definition
SSE / (n - k)
Term
MST
Definition
SST / (k - 1)
Term
Multiple linear regression
Definition
There is more than one explanatory variable.
Term
Nonparametric procedure
Definition

aka Distribution-free procedure

aka Sign test

aka Sign-ranked test

Used if distribution is not normal.

Term
Observed
Definition
The observed sample counts in a category.
Term
Paired difference t procedure
Definition
If the null hypothesis is true, t will have a distribution of n - 1 degrees of freedom.
Term
Permutation test
Definition
A method of inference for two means.
Term
Pooled sample proportion (p bar)
Definition
(X1 + X2) / (n1 + n2)
Term
Pooled-variance procedure
Definition
A method of inference for two means. Assumes equal population variances, and results in an exact method. Consistent with other common statistical procedures such as ANOVA and linear regression. Assumptions are likely to be untrue. Performs poorly if assumptions are violated, and even worse when there is a difference in sample sizes. Large sample sizes doesn't erase this problem.
Term
Prediction interval
Definition
Either predicting a single value of Y at a given X (confidence interval is a constant width), or estimating the theoretical mean of Y at a given X (confidence interval is narrower than the mean of X).
Term
Proportion
Definition
The mount of individuals in a population showing a certain measured characteristic.
Term
Regression analysis
Definition
Explores possible relationships between Y and X.
Term
Residual
Definition
The observed value minus the predicted value.
Term
Residual plot
Definition
A scatter plot of residuals.
Term
Response variable (Y)
Definition

aka Dependent variable

The variable we want to predict.

Term
Simple linear regression
Definition
There is one explanatory variable.
Term
SS(total)
Definition
SST + SSE
Term
SSE
Definition
The sum of squares within groups.
Term
SST
Definition
The sum of squares between groups.
Term
Test of independence
Definition
A chi-square test for a two-way table.
Term
Welch procedure
Definition

aka Unpooled-variance procedure

A method of inference for two means. Does not assume equal proportion variances, and results in an approximate method. Usable in a wider variety of situations. Does not require assumptions. Works better than pooled-varaince but is less exact.

Term
Welch-Satterthwaite approximation
Definition
A complex equation that gives the degrees of freedom in a Welch procedure.
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