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Avoid the Hustle

Probability, hypotheses, sampling distributions & standard erro

Category: Statistics

PART 1 – Please use the Vukicevic practice data set for tasks 2 to 6.
Task Activity (Please do not use Excel or any other package for
Part 1.)
Co-ordinator’s comment: The purpose of Task 1 is to provide practice in probability calculations. Probability theory is the basis of inferential statistics.

Task 1:
Please imagine you are studying cases of a rare genetic disease. Research suggests that 1 woman in 28 in the population carries the gene required for the disease, 1 man in 18 carries the gene, and there is 1 chance in 4 that a child of a couple who both possess the required gene will be affected. If there are 1.15 million couples of childbearing age in NSW, each of whom has a 1 in 22 chance of producing a child in 2014, calculate how many affected children are likely to be born to NSW citizens in 2014. Please show your calculations.
Co-ordinator’s comment: The purpose of Tasks 2 & 3 is to provide practice in devising and writing hypotheses.

Task 2:
We wish to decide if the Eccentric Viewing intervention changes people’s reading speed. Write out, in words AND in symbol form, an appropriate null hypothesis for the hand calculation practice data.
(Hint 1: Null and alternative hypotheses refer to the populations from which our samples come. Hint 2: Base the hypothesis on the column of change scores calculated for Assignment 1 Part 1.)

Task 3:
Write out, in words AND in symbol form, the alternative hypothesis for the null hypothesis in Task 2.
Co-ordinator’s comment: The purpose of Tasks 4 and 5 is to carry out a repeated-measures t-test (also called a within- subjects t-test, a paired t-test, a matched-samples t-test, a t- test for correlated samples, a dependent means t-test, or a dependent samples t-test.) In assignment 1 you used your impressions from descriptive statistics to decide if the Eccentric Viewing intervention was effective in the sample tested.
In these tasks you will use inferential statistics to estimate the probability that the Eccentric Viewing intervention is associated with changed reading speed in the population represented by the sample.

Task 4: This task uses the column of change (difference) scores you calculated for Assignment 1 Part 1.
Please compute the standard error of the mean for this column of scores. Please show your workings.

Task 5:
Please calculate the t value for the column of change scores from Task 4, showing your calculations. Comparing this calculated (obtained) value to critical values from tables, state whether to accept or reject the null hypothesis.

Task 6:
Briefly state in plain English (not statsbabble) what the t-test has told us about the Eccentric Viewing intervention i.e. is the intervention effective or not? (Hint: “Briefly” means “briefly”. It does not mean “write an essay”.)
6

ASSIGNMENT 2 PART 2 –

Please use the Ward & Sanson-Fisher
practice data set.
Co-ordinator’s comment: The purpose of Task 1 is to prepare for a single-sample t-test.

Task 1:
Please use the computer package to calculate the difference between pre and post workshop scores for each of the participants i.e. produce a new column of scores which are the change from pre workshop scores to post workshop scores. If you are using SAS please print the difference scores and show your SAS commands. If you are using SPSS or Instat+ please show your data spreadsheet.
Co-ordinator’s comment: Tasks 2 and 3 are doing with the statistics package what was done by hand in Part 1, Tasks 4 and 5.

Task 2:
Selecting only the Experimental group’s data from Task 1, carry out a t-test testing the null hypothesis that the Experimental group comes from a population in which there is no change in mean score after intervention. Show your output.

Task 3:
Briefly interpret the output from Task 2 i.e. Has the Experimental group changed after intervention? You should write your answer in plain English, not statsbabble. (Hint: “Briefly” means “briefly”. It does not mean “write an essay”.)
Co-ordinator’s comment: Now you are a little more familiar with your statistics package, Tasks 4 to 6 are catching up with crosstabulations (introduced in assignment 1).

Task 4:
In the computer package practice data set create a new data column in which you code each person as 0 (lower post score compared to pre score) or 1 (equal or higher post score than pre score). If you are using SAS, supply your command file. If you are using one of the other packages, print your data editor. Note: Instat+ users should code 1 and 2 instead of 0 and 1 respectively.

Task 5:
Using the computer package, please produce a 2 by 2 crosstabulation table. The two variables to be crosstabulated are, firstly, the two outcome groups you created in the previous task and, secondly, the experimental/control group coding. Have the statistics package calculate the row and column percentages for the crosstabulation table in the previous task. [Hint: In Part 1 of assignment 1 you produced a 2 x 4 crosstabulation table. The table in this task should look similar, except 2 x
2 rather than 2 x 4. If your table has more than 2 rows and 2 columns please revisit it.]

Task 6:
In no more than 250 words, comment on what you infer from the counts and percentages in the crosstabulation table from the previous task.