Statistical Analysis: Chi Square

Slides:



Advertisements
Similar presentations
The Chi Square Test A statistical method used to determine goodness of fit Goodness of fit refers to how close the observed data are to those predicted.
Advertisements

Lecture (11,12) Parameter Estimation of PDF and Fitting a Distribution Function.
Virtual Fly Lab AP Biology
AP Biology.  Segregation of the alleles into gametes is like a coin toss (heads or tails = equal probability)  Rule of Multiplication  Probability.
Chi-Square Test Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.
Quantitative Skills 4: The Chi-Square Test
Chi-square notes. What is a Chi-test used for? Pronounced like kite, not like cheese! This test is used to check if the difference between expected and.
Chi Square (X 2 ) Analysis Calculating the significance of deviation in experimental results.
Chi-square Goodness of Fit Test
The Chi-square Statistic. Goodness of fit 0 This test is used to decide whether there is any difference between the observed (experimental) value and.
AM Recitation 2/10/11.
Chi-Squared Test.
Chi-Square as a Statistical Test Chi-square test: an inferential statistics technique designed to test for significant relationships between two variables.
Chi square analysis Just when you thought statistics was over!!
Chi Square Analysis The chi square analysis allows you to use statistics to determine if your data “good” or not. In our fruit fly labs we are using laws.
Fruit Fly Basics Drosophila melanogaster. Wild Type Phenotype Red eyes Tan Body Black Rings on abdomen Normal Wings.
Statistical Analysis: Chi Square AP Biology Ms. Haut.
Chi-Square Analysis AP Biology.
Science Practice 2: The student can use mathematics appropriately. Science Practice 5: The student can perform data analysis and evaluation of evidence.
Chapter 13 Understanding research results: statistical inference.
Did Mendel fake is data? Do a quick internet search and can you find opinions that support or reject this point of view. Does it matter? Should it matter?
DRAWING INFERENCES FROM DATA THE CHI SQUARE TEST.
Chi Square Pg 302. Why Chi - Squared ▪Biologists and other scientists use relationships they have discovered in the lab to predict events that might happen.
Chi-Square (χ 2 ) Analysis Statistical Analysis of Genetic Data.
Hypothesis Testing Hypothesis vs Theory  Hypothesis  An educated guess about outcome of an experiment  Theory  An explanation of observed facts that.
Inference for Tables: Chi-Squares procedures (2 more chapters to go!)
Chi-Square Analysis AP Biology.
Warm up On slide.
The Chi Square Test A statistical method used to determine goodness of fit Chi-square requires no assumptions about the shape of the population distribution.
Chi-Squared (2) Analysis
Statistical Analysis: Chi Square
Chi-Squared Χ2 Analysis
M & M Statistics: A Chi Square Analysis
Virtual Fly Lab AP Biology
Chi Square Analysis The chi square analysis allows you to use statistics to determine if your data “good” or not. In our fruit fly labs we are using laws.
Fruit Fly Genetics Drosophila melanogaster
Analyzing Data c2 Test….”Chi” Square.
Virtual Fly Lab AP Biology
Chi-Square Analysis AP Biology.
Inferential Statistics
Chi-Square Test.
The Chi Square Test A statistical method used to determine goodness of fit Goodness of fit refers to how close the observed data are to those predicted.
Chi Square SBI3UP.
MENDELIAN GENETICS CHI SQUARE ANALYSIS
Analyzing Data c2 Test….”Chi” Square.
UNIT 6: MENDELIAN GENETICS CHI SQUARE ANALYSIS
The Chi Square Test A statistical method used to determine goodness of fit Goodness of fit refers to how close the observed data are to those predicted.
Chi square.
Chi-Square Analysis.
Chi-Square Test.
Chi Square Analysis The chi square analysis allows you to use statistics to determine if your data is “good” or not. In our fruit fly labs we are using.
Chi-Square Analysis AP Biology.
The Chi Square Test A statistical method used to determine goodness of fit Goodness of fit refers to how close the observed data are to those predicted.
Chi Square Analysis The chi square analysis allows you to use statistics to determine if your data is “good”. In our fruit fly labs we are using laws of.
P-VALUE.
Chi-Square Test.
Chi-Square Analysis AP Biology.
Chi2 (A.K.A X2).
Chi-Square Analysis AP Biology.
How do you know if the variation in data is the result of random chance or environmental factors? O is the observed value E is the expected value.
UNIT V CHISQUARE DISTRIBUTION
S.M.JOSHI COLLEGE, HADAPSAR
Chi Square Analysis The chi square analysis allows you to use statistics to determine if your data “good” or not. In our fruit fly labs we are using laws.
Graphs and Chi Square.
Chi square.
Chi-Square Analysis AP Biology.
Mortality Analysis.
Will use Fruit Flies for our example
Presentation transcript:

Statistical Analysis: Chi Square

“Goodness of Fit Test” Chi Square (χ2) Statistical analysis used to determine whether data obtained experimentally provides a “good fit” to the expected data Used to determine if any deviations from the expected results are due to random chance alone or to other circumstances

Null Hypothesis- Ho (in a statistical test) the hypothesis that there is no significant statistical difference between specified populations any observed difference being due to sampling or experimental error.

Chi Square (χ2) Use the equation to test the “null” hypothesis The prediction that data from the experiment will match the expected results χ2 = Σ (observed results – expected results)2 expected results When all else is equal, the value of χ2 increases as the difference between the observed and expected values increase

Chi Square (χ2) Once you have calculated the value of χ2, you must determine the probability that the difference between the observed and expected values (χ2) occurred simply by chance (sample error) You compare the calculated value to the appropriate value in a “degrees of freedom” table

Degrees of Freedom df P = 0.05 P = 0.01 P = 0.001 1 3.84 6.64 10.83 2 Degrees of freedom = # of categories – 1 Takes into account the natural increase in χ2 as the number of categories increases df P = 0.05 P = 0.01 P = 0.001 1 3.84 6.64 10.83 2 5.99 9.21 13.82 3 7.82 11.35 16.27 4 9.49 13.28 18.47 5 11.07 15.09 20.52 6 12.59 16.81 22.46 7 14.07 18.48 24.32

Why subtract 1? The degrees of freedom are the number of values that are free to vary in the data set. For example: Q. Pick three numbers that have a mean (average) of 10. A. Some sets of numbers you might pick: 9, 10, 11 or 8, 10, 12 or 5, 10, 15. Once you have chosen the first two numbers in the set, the third is fixed. In other words, you can’t choose the third item in the set. The only numbers that are free to vary are the first two. So degrees of freedom for a set of three numbers is TWO.

Practice Problem A newly identified fruit fly mutant, cyclops eye (large and single in the middle of the head), is hypothesized to be autosomal dominant. The experimenter started with homozygous wild type and homozygous cyclops. The second generation is heterozygous. The data from the F2 generation was 104 wild type and 260 cyclops. ( since it is autosomal dominant you do not need to worry about the sex of the flies) Does this data support or reject the hypothesis? Use chi square to prove your position.

χ2 = Expected: E = cyclops e = normal P = EE x ee F1 = all Ee F2 = Ee x Ee 3: cyclops:1 normal Out of 364 offspring we should get an expected ratio of 273 cyclops: 91 normal What we actually got was 260 cyclops: 104 normal χ2 = (260-273)2 (104-91)2 + 273 91 = 169/273 + 169/91 = 0.61 + 1.86 = 2.48

χ2 = 2.48 Do we accept the hypothesis? Reject χ2 = 2.48 Do we accept the hypothesis? Accepted: pattern of inheritance is autosomal dominant

                    Null Hypothesis: If the Mars Co. M & M sorters are doing their job correctly, then there should be no difference in M & M color ratios between actual store-bought bags of M &Ms and what the Mars Co. claims are the actual ratios. Let’s test this next class!