20/21: Correlation

Start at the beginning again:

• • We created a 95% Confidence Interval in Class:

    • using the formula x-bar +- z* (sd/sqrt(n))

  • This gives us an approximation of what the true mean is.

  • Let's try with some new numbers:

  • Newts: Some newt data (from The Basic Practice of Statistics, by David Moore):

    • Biologists studying the healing of skin wounds measured at the rate at which new cells closed a razor cut made in the skin of an anesthetized newt. Here are the data from 18 newts, measured in micrometers (millionths of a meter) per hour:

      • 29 27 34 40 22 28 14 35 26 35 12 30 23 18 11 22 23 33

        • We know from previous experiments that the sd for newts healing is 8 micrometers per hour.

  • Ancient air. The composition of the earth's atmosphere may have changed over time. To try to discover the nature of the earths atmosphere long ago, we try to examine the gas in bubbles inside the ancient amber. The gas has been trapped (by estimates at least) an average of 75 to 95 million years. Below is the percent of nitrogen that is stored in these samples air bubbles:

    • • 63.4, 65.0, 64.4, 63.3, 54.8, 64.5, 60.8, 49.1, 51.0

      • The air currently has a percent of 78.1 nitrogen. [according to wikipedia]

2) p-value:

cutting newts with NEWT SALVE 2000!

• I have created this amazing newt salve, called NEWT SALVE 2000. It is supposed to help newts heal at a faster rate than they did before. Here are the healing times:

23 27 31 39 27 23 42 30 30 44 18 28 32 28 28 29

• • • • The big question becomes--do I know that this data actually shows that the newt salve does work? I can't know if the difference is in the population itself that I chose at random, the things I chose, or just because these newts were having a good day.

      • And so I set up some hypothesis testing.

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stop watch names

plotting bivariate data

• • • • • explanatory vs. response

        • independent vs. dependent

        • what is correlation

          • picture from wikipedia: http://upload.wikimedia.org/wikipedia/commons/d/d4/Correlation_examples2.svg

          • guess the correlation

            • correlation and point calculator: http://illuminations.nctm.org/Activity.aspx?id=4186

            • sites used in class:

            • http://www.ruf.rice.edu/~lane/stat_sim/reg_by_eye/

            • http://www.math.usu.edu/~schneit/CTIS/scorrelation/

            • http://istics.net/stat/correlations/

        • correlation vs. causation picture

        • http://i.imgur.com/PedqQ.jpg

        • http://i.imgur.com/h2JCluxl.jpg

        • http://xkcd.com/552/

Question: How many folds to the moon?

Linear vs. exponential.

goldfish and paper plates.