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Statistics I:   Learning Objectives

 

Instructor:    Raoul A. Arreola, Ph.D.

 

PART 1: Descriptive Statistics

   A. Describing Data

 

1. The student will be able to define (verbally and/or symbolically) the following terms:
1. Parameter
2. Statistic
3. Population
4. Random Sample
5. Variable
6. Mean
7. Median
8. Mode
9. Range
10. Average (mean) Deviation
11. Variance (standard deviation)

 

2. Given a group of graphical illustrations of various distributions the student will be able to correctly identify each of the following types of distributions:
1. Negatively skewed
2. Positively skewed
3. Leptokurtic
4. Platykurtic
5. Bimodal
6. Normal

 

3. Given a finite population of size N, the student will be able to correctly compute each of the following:
1. 
2. Median
3. Mode
4. ²
5. s²
6. Range
7. Average (mean) deviation
8. ²_x+b , ²_ax , ²_x+y  (where x and y are independent random variables)

 

4. Given a finite population or a random sample of observations, the student will be able to define and/or calculate the following:
1. Mean, Median, Mode
2. Range, Mean Deviation, Variance

 

5. Given the mean and variance of two independent random variables X and Y, and integer constants (a) and (b), the student will be able to calculate the mean and variance of:
1. (aX + b)
2. (X + Y)

 

6. Given a set of observations the student will be able to:
1. Sketch a histogram, frequency polygon, cumulative frequency polygon, and percent ogive curve.
2. Correctly describe any frequency polygon using the following terms:

                                               i.     Unimodal

                                             ii.     Bimodal

                                            iii.     Symmetrical

                                            iv.     Negatively skewed

                                             v.     Positively skewed

 

7.     Given a frequency distribution (either grouped or ungrouped) the student will be able to calculate the specific percentile and percentile rank for any given observation in the distribution.

 

 

   B. Pearson Product-Moment Correlation

 

8.     Given a description of a situation in which the degree of association between two variables is desired, the student will be able to correctly:

1. Identify the variables to be correlated
2. Determine whether the variables are continuous or discrete
3. Identify the level of measurement employed with each variable

 

9. Given two sets of raw scores the student will be able to plot the appropriate bivariate distribution using the Cartesian coordinate system.

 

10. Given a plot of a bivariate distribution the student will be able to correctly identify it as representing one of the following:
1. Positive linear relationship
2. Negative linear relationship
3. Curvilinear relationship
4. No relationship

 

11.  The student will be able to correctly state the three basic assumptions underlying the Pearson Product-Moment correlation.

 

12. Given a set of ten descriptions of situations which require the determination of the degree of association between two variables, and given that only four of these situations meet all the assumptions for the computation of the Pearson Product-Moment correlation, the student will be able to correctly identify those four situations and correctly indicate why the Pearson Product-Moment correlation may NOT be legitimately computed in each of the remaining six situations.

 

13. The student will be able to correctly explain, by means of a plot of a bivariate distribution, the effects of restricting the range on the size of the correlation.

 

14. Given a description of a "real life" situation with appropriate data, the student will be able to compute the Pearson Product-Moment correlation coefficient.

 

   C. Linear Regression

 

15. The student will be able to explain, in his or her own words, the regression toward the mean phenomenon, noting particularly how and why it occurs (in terms of true plus chance scores).

 

16. The student will be able to correctly write the basic linear regression model, correctly identifying the criterion, the prediction variable and the appropriate constants.

 

17. Given a description of a "real life" situation in which the prediction of one variable from another is desired, the student will be able to:
1. Identify the dependent and independent variables
2. Compute the appropriate linear regression equation constants for the equation predicting the dependent variable from the independent one.
3. Compute the standard error of estimate for the regression equation.

 

18. Given a linear regression equation and its corresponding standard error of estimate, the student will be able to:
1. Predict the corresponding score on the dependant variable given an individual's score on the independent variable.
2. Make a probability statement as to the possible error of the resulting prediction.

 

 

PART 2: Inferential Statistics

General Objectives:

Given a description of a realistic situation in which some statistical analysis is appropriate, the student will be able to state a statistical hypothesis relevant to the situation, state an alternative hypothesis, and identify a critical region.  Having done this, the student will be able to select the appropriate statistical test to employ, successfully execute the test, and make a decision based on the outcome of the test.  The student should then be able to interpret that decision in terms of action that should or should not be taken, and the probable consequences of that action.

 

Second Order Objectives

 

Case I:    Given a set of sample data, the student will be able to test:

H_o:  The sample scores came from a population with a specified mean ( = ₀)

H₁:  The sample scores came from a population with a mean NOT equal to some specified value ( ₀)

 

Case II:   Given a data for two samples X and Y, test the following:

a.  H_o:  The population variance of X equals the population variance of Y ( )

H₁:  The population variance of X does NOT equal the population variance of Y ( )

 

b. H_o:  The population mean of X equals the population variance of Y ( )

H₁:  The population mean of X does NOT equal the population mean of Y ( )

 

 

Case III: Given pre-test and post-test scores for a sample, the student will be able to test:

a.  H_o:  The population mean of the post-test equals the population mean of the pre-test ( )

    H₁:  The population mean of the post-test is greater than the population mean of the pre-test ( )

 

b. Compute the Pearson Product-Moment correlation between the two sets of scores.

 

c.  Find the 95% confidence interval about the value in (b) above, making an appropriate interpretive probability statement about the value.

 

 

 

Case IV: Given appropriate data from three groups, X, Y and Z, the student will be able to successfully test the following hypotheses:

 

a.  H_o:  There is no difference in the distribution of grades received by males and females in any of the three groups

H₁:  There is a difference in the distribution of grades received by males and females in the three groups.

 

b. H_o:  The population mean of group X equals the population mean of group Y equals the population mean of group Z ( )

H₁:  At least one pair of the above three means is not equal.