Chi-square goodness of fit tests Chi-square goodness of fit.

Chi-square goodness of fit tests

Chi-square goodness of fit testsChi-square goodness of fit

Context you can use chi-square tests- genetic inheritance hypothese, tell if a die is fair, tell if search committee is biased in selecting candidates2Core issue in statistics: When are you viewing just random noise and when is there a real trend?Chi-square goodness of fit

This is the sex ratio we expect in the population3Core issue in statistics: When are you viewing just random noise and when is there a real trend?Chi-square goodness of fit

If you end up with a sample with two women, this could very well just be noise4Core issue in statistics: When are you viewing just random noise and when is there a real trend?Chi-square goodness of fit

What about 3 women? Or 5?5Core issue in statistics: When are you viewing just random noise and when is there a real trend?Chi-square goodness of fit

Or a sample of 12 made up of all women? This last scenario seems to be an obvious deviation from random. A chi-square test helps you find the tipping point- you dont just have to rely on your common sense6Your response variable is count dataWhen to use a chi-square testYour response falls into different categoriesYou have a hypothesis for the responses you expectYou want to know if the difference between the responses you observe and the responses you expect is significant or notIf the test tells you your data is not significantly different from what you expect, you support the hypothesisHow to interpret a chi-square testIf the test tells you your data is significantly different from what you expect, you reject the hypothesisNo statistical test ever proves a hypothesis.What is chi-square?x2 = Chi-square value = Sum ofx2 = (Observed Value Expected Value)2Expected Value

ObservedExpectedObs-Exp(Obs-Exp)2(Obs-Exp)2ExpCategory 1Category 2..X2 totalDegrees of FreedomExample problem #1Work through example problem 1 from the work sheet in small groups or as a class. Reconvene when it comes time to read the chi-square table and demo how this is done on the next several slides10Chi-square probability table0.990.950.90.80.70.60.50.40.30.20.10.050.01df10.00010.0030.0150.0640.1480.2750.4550.7081.071.642.713.846.6320.0200.1030.2110.4460.7131.021.391.832.413.224.615.999.2130.1150.3520.5841.001.421.872.372.953.674.646.257.8111.340.2970.7111.061.652.192.753.364.044.885.997.789.4913.350.5541.151.612.343.003.664.355.136.067.299.2411.115.160.8721.642.203.073.834.575.356.217.238.5610.612.616.871.242.172.833.824.675.496.357.288.389.8012.014.118.581.652.733.494.595.536.427.348.359.5211.013.415.520.1Chi-square probability table0.990.950.90.80.70.60.50.40.30.20.10.050.01df10.00010.0030.0150.0640.1480.2750.4550.7081.071.642.713.846.6320.0200.1030.2110.4460.7131.021.391.832.413.224.615.999.2130.1150.3520.5841.001.421.872.372.953.674.646.257.8111.340.2970.7111.061.652.192.753.364.044.885.997.789.4913.350.5541.151.612.343.003.664.355.136.067.299.2411.115.160.8721.642.203.073.834.575.356.217.238.5610.612.616.871.242.172.833.824.675.496.357.288.389.8012.014.118.581.652.733.494.595.536.427.348.359.5211.013.415.520.1Only 5% chance that the difference between your obs and exp values comes from chance alone

Your hypothesis can be rejectedChi-square probability table0.990.950.90.80.70.60.50.40.30.20.10.050.01df10.00010.0030.0150.0640.1480.2750.4550.7081.071.642.713.846.6320.0200.1030.2110.4460.7131.021.391.832.413.224.615.999.2130.1150.3520.5841.001.421.872.372.953.674.646.257.8111.340.2970.7111.061.652.192.753.364.044.885.997.789.4913.350.5541.151.612.343.003.664.355.136.067.299.2411.115.160.8721.642.203.073.834.575.356.217.238.5610.612.616.871.242.172.833.824.675.496.357.288.389.8012.014.118.581.652.733.494.595.536.427.348.359.5211.013.415.520.150-60% chance differences are from random chanceExample problem 2Female Song Worksheet

Bird song: Its not just for males anymore

Male house wrens sing to attract matesand defend territories

Females sing a lot too!

Why?

Background info for house wren worksheet16Why do females sing?H1: To help coordinate their behavior with their male

Prediction

Why do females sing?H2: To solicit copulations from the malePrediction

http://farm9.staticflickr.com/8251/8690727079_f1ce1a7c47_z.jpg18Why do females sing?H3: To defend their nests against other house wrensPrediction

http://farm9.staticflickr.com/8251/8690727079_f1ce1a7c47_z.jpg19Why do females sing?Null hypothesis: Female song occurs randomlyPrediction

http://farm9.staticflickr.com/8251/8690727079_f1ce1a7c47_z.jpg20