Available online
Description
This programme takes the distribution of marks from two tests, verbal aptitude and comprehension and considers the construction of a bi-variate normal distribution.
This programme takes the distribution of marks from two tests, verbal aptitude and comprehension and considers the construction of a bi-variate normal distribution.
| Module code and title: | M341, Fundamentals of statistical inference |
|---|---|
| Item code: | M341; 02 |
| First transmission date: | 21-04-1977 |
| Published: | 1977 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:26 |
| + Show more... | |
| Producer: | Denis Gartside |
| Contributors: | Angela Dean; Ross Renner |
| Publisher: | BBC Open University |
| Keyword(s): | Bivariate; Conditional distributions; Correlation; English language tests; Normal distributions; Probability density functions |
| Footage description: | Still shots of third world students who have applied for university places in Britain undergoing a battery of English language tests. Ross Renner introduces the programme by outlining the statistical problem of comparing the results of these tests with those of their English counterparts. Renner shows two specimen questions from each of the two tests given to students. While doing so, he explains how the tests work. Next, looking at a computer print-out which has data from similar tests done on 10,000 British students, Renner explains what might be done with the data. Angela Dean identifies the underlying sample space for the probability model she attempts to build up for the student data above. Several graphic aids, some animated (including scatter diagrams), are used. She shows a 3 dimensional model of a relative frequency distribution and from this she arrives at a probability density function. Dean goes on to identify the marginal relative frequency distribution. Ross Renner with the block model of a marginal relative frequency distribution. The histogram of this distribution is plotted by the graph plotter. Renner then plots a normal curve on top of the histogram and explains how one determines if the curve is a good approximation of the data. Renner compares tables of predicted and observed frequencies obtained by this method. Angela Dean uses a model to explain how four conditional PDPs are obtained from a probability model. Ross Renner transforms the test data to standardised scores. Animated scatter diagrams show ordered pairs of test results after transformation. He goes on to a display of means and standard deviations for the distribution of data. The graph plotter is then used to plot a histogram of the class section with a midpoint of 65.5. A normal distribution curve is then plotted over this. Renner comments on the fit. Assuming that the conditional distributions of Z2 given each value of Z, are normal, Renner sums this up in one conditional PDF. Shots of regression curve on an animated graph. Angela Dean uses a physical model of a probability distribution to sum up the properties of the distribution of student marks. |
| Master spool number: | 6HT/72285 |
| Production number: | 00525_4231 |
| Videofinder number: | 1113 |
| Available to public: | no |
