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Randomized comparative experiments; The principles of experimental design

Randomized comparative experiments; The principles of experimental design. AP Statistics. Randomized comparative experiments. Randomization produces groups of experimental units that should all me similar in respects before the treatments are applied.

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Randomized comparative experiments; The principles of experimental design

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  1. Randomized comparative experiments;The principles of experimental design AP Statistics

  2. Randomized comparative experiments • Randomization produces groups of experimental units that should all me similar in respects before the treatments are applied. • Comparative design ensures that influences other than the diets operate equally on both groups.

  3. Principles of Experimental Design • The basic principles of statistical design of experiments are • Control the effects of lurking variables on the response, most simply by comparing two or more treatments. • Randomize – use impersonal chance to assign experimental units to treatments. • Replicate each treatment on many units to reduce chance variation in results. • An observed effect so large that it would rarely occur by chance is called STATISTICALLY SIGNIFICANT.

  4. Example 5.12 p. 295 A food company assesses the nutritional quality of a new instant breakfast product by feeding it to newly weaned male white rats. The response variable is a rat’s weight gain over a 28 day period. A control group of rats eats a standard diet, but otherwise receives the same treatment as the experimental group. We must first randomly assign the rats to the two different groups (the control group and the experimental group). To do this, we choose an SRS of 15 rats from the population of 30 rats.  • Lets use Table B starting at line 130 • Label the rats 01-30 and randomly select 15 rats to be in our control group. (the remaining 15 are in our experimental group) • 69051 64817 87174 09517 84534 06489 87201 97245 • 05007 16632 81194 14873 04197 85576 45195 96565 • 68732 55259 84292 08796 43165 93739 31685 97150 • 45740 41807 65561 33302 07051 93623 18132 09547 • 27816 78416 18329 21337 35213 37741 04312 68508 • We have selected rats 5, 16, 17, 20, 19, 04, 25, 29, 18, 07, 13, 02, 23, 27, and 21 for our control group. (Call it Group 2) • We will place the remaining 15 rats into our experimental group

  5. Here is the mapping for our experiment and sampling • Here, all of our experimental units have been allocated at random among the treatments. Therefore, our experiment is completely randomized.

  6. Lurking variables • Identifying lurking variables can be fun and helpful. As appropriate randomization is applied in an experiment, it eliminates the effects of the lurking variables on our experiment. For instance: • Example: • Studies show that there is a strong correlation between the amount of firefighters at a fire and the amount of damage done. This has led some to conclude that sending more firefighters actually causes more damage. • This doesn’t make sense at all. Let us identify some lurking variables that may be causing this correlation

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