Statistical Analysis Question - Sex Ratio...Chi Squared?
8d) Ho formulated is that there is NO significant difference between observed and expected sex ratio. Level of significance = alpha = a = 0.05 Test criterion is Chi-square test. Observed number (O) of red birds: Males 30 and Females 19 Total = 49 Expected number (E) of red birds: Males 50% of 49 = 24.5 and Females 50% of 49 = 24.5 Calculated value of Chi-square = sigma ((O-E)^2/E) = (30-24.5)^2/24.5 + (19-24.5)^2/24.5 = 1.235 + 1.235 = 2.470 Degrees of freedom = v = n-1 = 2-1 = 1 Critical value of Chi-square for v = 1 at a = 0.05 is 3.84 Since the calculated value of chi-square (2.47) is less than the critical value at a = 0.05 (3.84), the Ho will be accepted. In Other words there is NO evidence to reject the Ho. It can be inferred that the sex ratio in the red birds does not differ from expectation. >>>>>>>>>>>>>>>>>>>>>>> In order to obtain a significant chi-square, the calculated chi-square value should be > the critical value of chi-square (3.84) Assume the number of male birds = x and female birds = (49-x) calculate the chi-square as above then develop an inequality i.e., > 3.84 solve for x
These are first level topics that are part of a general data science interview, where statistics is one of the skills being brushed over, but not the primary one. These are not for evaluating expertise in statistics, just familiarity and reasonable coherence to apply correctly. Data explorationHow do you summarize the distribution of your data?How do you handle outliers or data points that skew data?What assumptions can you make? Why and when? (i.e When is it safe to assume "normal")Confidence intervalsHow they are constructedWhy you standardize How to interpret SamplingWhy and when?How do you calculate needed sample size? [Power analysis is advanced]LimitationsBootstrapping and resampling? BiasesWhen you sample, what bias are you inflicting?How do you control for biases? What are some of the first things that come to mind when I do X in terms of biasing your data?ModelingCan you build a simple linear model? How do you select features?How do you evaluate a model?Experimentation How do test new concepts or hypotheses in....insert domain X? i.e. How would evaluate whether or not consumers like the webpage redesign or new food being served? How do you create test and control groups?How do you control for external factors?How do you evaluate results?
Chi square test help! Statistics!?
a) H0: There is no difference in the distribution of violent crimes between 2000 and last year. H1: There is a difference in the distribution of violent crimes between 2000 and last year. b) If H0 is true, we expect 25% of 500 for each of the above-mentioned crimes. Murder = E(1)= 500(0.25) = 125 Rape = E(2) = 125 Robberies = E(3) = 125 Assaults = E(4) = 125 c) Observed --- Expected 5 ------------125 25-----------125 150---------125 320---------125 I have multiplied the observed percentages by 500 since we do not have the population size. Test statistic x^2 = Σ ([O[i]-E[i])^2 /E[i] Rejection region: If computed chi-square exceeds critical x^2 with 3 degrees of freedom (assume 5% level of significance), the critical chi-squared is :7.81 Reject H0 if computed x^2 >= 7.81 x^2 = (5-125)^2/125+(25-125)^2/125+(150-125)^2... =504.4 d) p-value cannot be computed directly. Look up the chi-squared table with 3 degrees of freedom and locate 504.4 and locate the significance backwards. p-value < 0.0005. Therefore, reject H0 and conclude there is a difference in the distribution of violent crimes between 2000 and last year.
Hypothesis testing and test statistics?
Tuff question. The question itself is not difficult. However, you are in the realm of "opinion" as to the best way to proceed of many possible ways. Without the answers, it would have been impossible for me to proceed at all. I'm gonna hafta take some guesses as to how it was done. First of all, there is NO hypothesis concerning the mean and s.d. The only question here is, "Is the distribution a normal distribution." or better still, "Do we have reason to believe the distribution is non normal?" There are several test statistics available to test this hypothesis. Probably the most common (when I was growing up many years ago) would be the Chi Square Test. Given the critical value of 7.81, I suspect that is what they want you to use. Were it Chi Square, it would involve "breaking up" the sample into various segments and comparing those segments to what would be expected under normal curve assumptions. For example, we could consider that the "normal curve" would have 34% between 1 s.d. of the mean and the mean, and 16% outside that range. Clearly, the number of classes is arbitrary. Since they used 7.81 as a critical value, (3 degrees of freedom), I presume they broke the curve up into 4 parts. We could then say that we would expect: 34% x 30 = 10.2 observations between the mean and 1 s.d., and 4.8 outside that range. So, if we broke the curve up into 4 parts, we would expect: 4.8....10.2....10.2....4.8 observations in each of the four catagories (where the dots are for formatting) NOW, we can look at our "observed" data and determine how many are in each of the ranges. mean 23.07 s.d. 4.29 less than 18.78 // (less than 1 s.d.) 18.78 - 23.07 ///// ///// ///// /// (between -1 s.d. and mean) 23.07 - 27.36 ///// (between mean and 1 s.d.) greater than 27.36 ///// ( more than 1 s.d.) Now, your observed table will be: 2....18....5....5 and you can compute Chi Squared. 4.8....10.2....10.2....4.8........expe... table 2.........18........5........5........... table I could not obtain their answer for the test statistic. I got 10.26 Since 10.26 is greater than 7.81, we conclude "non normality". hope this helps, tony
Can you solve these statistics questions?
95% of all scores will fall in the range of the average +/- 3 standard deviations (approximately). You can find this result in any good text on statistics. Therefore children with an IQ > 145 will be in the top 5%. I'm not sure how you're defining 'middle 95%', but assuming it's the 95% that leaves the tails on both ends of the distribution symmetrical, then 100-45 = 55 ... lower than this is 'abnormal' on the low end 11+45 = 145 ... higher than this is 'abnormal' on the high end
Chi-Square Stats Question - Cola (Please Help)?
Chi-Square Stats Question - Cola (Please Help)? Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.) Cola Correct? Regular Cola Diet Cola Row Total Yes, got it right 7 7 14 No, got it wrong 12 20 32 Col Total 19 27 46
Data analysis (statistics) question regarding statistical testing?
It's D. You'll have two sets of measurements, with sizes n1 and n2, sample means m1 and m2, and sample standard deviations s1 and s2. You'll be testing to see if there is a significant difference in the sample means. The samples don't have to be the same size. It isn't C because the samples are independent -- each person is in only one group and there is no relationship between a person in group 1 to a person in group 2. It isn't A because you're not comparing measurements to a set of expected values or values from a known distribution. It isn't B because the samples aren't neccessarily the same size and, as stated earlier, there's no connection between a person in group 1 to a person in group 2. It would be impossible to make an x-y scattergram.
How do I do a Chi-Square test in Excel 2007?
First off, you might wish to make sure that you have the Analysis ToolPak installed. Within the Data ribbon, Excel’s Data Analysis add-in should appear as a menu item. If it does not, load the Data Analysis module as follows: • Click the Microsoft Office button at the upper left corner of the screen. • Click the Excel Options button. • Click Add-Ins. • Be sure that Excel Add-Ins appears in the Manage box, then click Go. • In the Add-Ins Available box, select Analysis ToolPak and click OK. The Analysis ToolPak should now be available for use. If you get a prompt indicating that the Analysis ToolPak is not installed on your computer, click Yes to install it. Once you enter in the separate Columns of Yes and No counts for all of the Rows with each Condition. Then it is a matter of using those counts to create your statistical analysis. But you did not mention which "Chi-Square Test" you are wishing to use: • for Goodness of Fit • Goodness-of-Fit Test for Normality • for Independence of Variables • Comparing Proportions From Independent Samples • Etc... If you are unfamiliar with the Chi-Square test and how it works, then there are Add-Ins available which will do everything for you. For example: http://www.analyse-it.com/support/documentation/220/standard/chi_square_test.htm If you need to know how to set this up yourself, then may I suggest downloading an eBook in PDF format "The Excel 2007 Data & Statistics Cookbook" which will have the information you need (see chapter 10): http://www.acrobatplanet.com/go/Excel_2007_Data_Statistics_Cookbook.pdf
That's a great question that a lot of people tend to ask in the data analytics realm. Truth is we have awesome tools, but alot of the really awesome tools don't have an exact, tangible meaning to others. We tend to call the ability to change data into actionable insight an art.For your specific question anything beyond regression meaning correlation, hypothesis, principal component analysis, SVMs, etc., is not interesting to execs/clients. These are all great things for your team to know and do, but KPIs (analytics), how to improve KPIs (statistics/predictions), and whether or not those improvements actually did improve KPIs (more analytics) is what pleases execs, because that's what they're performance is measured by. How this is done whether by statistics, gut feelings, or even magic, doesn't matter since the performance of your predictions is most likely what your performance is measured by, so its in your own best interest to use the best technology and methods that you feel work.