(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[During your stay, you have to evaluate whether the MagicFood, a new fertilizer, should be developed or not. You need to know whether it is better than another one, which was developed by another company several years before.
Of course, if the MagicFood gives better results than the other fertilizer, your may get a place in the company. But if you demonstrate the superiority of your product and that the farmer do not perceive the increase in productivity, you will likely loose the job…
You have a budget of 2000€. You can use this money to pay your former teacher who is now consultant in statistics.
During your stay, your colleagues will note your decisions and report your mistakes and good ideas to your boss. Your "//trust index//" starts at level 50.
Finally, you will have a QCM examination on Moodle (two trials possibles).
QCM and //trust index// will be used by your boss to decide about your future.
Good luck!]]
(bg:(hsl:0,1,0.8941,0.6))[[In order to give an answer to the issue (efficiency of MagicFood), you immediately think to an ideal solution->S2.IdealSolution]]
(set: $TrInd to 50)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"blink")[//Your present trust index is: $TrInd//]]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")
(set: $TrStateTer to "OK")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[The best way to address this issue would be to try the new fertilizer on a group of plants and to compare the harvest both to plants which did not receive it and to others receiving the competing one. However, you are not allowed to perform an experiment by using products of the competing company.
The only thing that you can do is to compare the harvest of a group of plants receiving the MagicFood with another which did not receive it. Then, you can compare these results to the results presented in a press release published by the competing company.]]
(bg:(hsl:0,1,0.8941,0.6))[[You read the press release->S3.PressRelease]]
(text-colour:black)[
Our company is pleased to inform you that we developed the StronGrow, a new fertilizer.
With StronGrow, the weight of harvested plants is significantly increased, and as measured by the Cohen's d (1.05), we can certify that the benefit is large as compared to untreated plants.
Moreover, the number of harvested plants is equivalent to the proportion observed in plants cultivated without fertilizer (about 62%) indicating the absence of toxicity.
]
(bg:(hsl:0,1,0.8941,0.6))[[You design your experiment->S4.YourExperiment]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[You design an experiment where 1000 feet of the plant are planted and treated with your new fertilizer, and 1000 feet are planted without fertilizer. Other experimental conditions are counterbalanced between the two groups. After a given time lapse, you harvest and measure the weight of each plant.]]
(bg:(hsl:0,1,0.8941,0.6))[[You finally get the data of your experiment->S5.YourResults]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[''Run R software''
''Load'' the datafile "Fertilizer.txt" In R
''Explore'' data organization (with head(), str()...).
The first column of this file indicates the group ("Control" or "Fertilizer"), the second indicates whether the plant survived until the harvest or not ("Alive" or "Dead"), and the third one indicates the weight of each harvested plant.]]
(bg:(hsl:0,1,0.8941,0.6))[[Now, you have to choose a statistical procedure to test the effect of MagicFood->S6.ChooseTest]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Which statistical procedure will you use to know whether the fertilizer increases the mean weight of the plants?]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[Test on ranks (Wilcoxon-Mann-Whitney)->S7.Wilcoxon]]]
(bg:transparent)[● [[Assessment of normality with a Shapiro-test->S11.Normality]]]
(bg:transparent)[● [[Student t test->S15.Student]]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[You choose to perform a Wilcoxon-Mann-Whitney test.
Please compute this test with R and note the W statistic and the p-value.
You should find W = 113710. Elsewhere you did not compute it properly and you should try again.
When you find the W = 113710 please check the p-value and click on the sentence corresponding to your conclusion:]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[The difference in means is significant->S9.BadWilcox]]]
(bg:transparent)[● [[The difference in means is not significant->S8.BadWilSign]]]
(bg:transparent)[● [[The difference in rank sum is significant->S10.GoodWilcox]]]
(bg:transparent)[● [[The difference in rank sum is not significant->S8.BadWilSign]]]]
(set: $TrState to "KO")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[You choose to perform a Shapiro test on both groups.
Please compute this test with R and note the W statistic and the p-value for each group.
You should find W = 0.847 and W = 0.880. Elsewhere you did not compute them properly and you should try again.
When you find the right values please click on the sentence corresponding to your conclusion:]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[In both groups, the distribution is significantly normal->S13.BadShap]]]
(bg:transparent)[● [[In both groups, the distribution significantly deviates from normality->S14.GoodShap]]]
(bg:transparent)[● [[In both groups, the distribution does not significantly deviates from normality->S12.BadShapSign]]]
(bg:transparent)[● [[In both groups, the distribution is not significantly normal->S12.BadShapSign]]]]
(set: $TrState to "KO")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Congratulations! You are on the right way!]]
(bg:(hsl:0,1,0.8941,0.6))[(bg:transparent)[[If you are puzzled, if you suspect that there is a mistake in the game, please click here->S16.Puzzled]]]
(bg:(hsl:0,1,0.8941,0.6))[(bg:transparent)[[Please compare the means of weights with a Student/Welch test and click here->S17.StudRes]]]
(if: $TrState is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Mmmh!... Are you sure? The first step when a Wilcoxon test is computed is to transform the data in ranks. So, it is no more possible to talk about means.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please do the same response but by talking about rank sums!->S7.Wilcoxon]]
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Wow!... Did you properly check your p-value ???]]
(bg:(hsl:0,1,0.8941,0.6))[[Check again !->S7.Wilcoxon]]
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Good! The Wilcoxon-Mann-Whitney test is significant (p<2.2 e10-16).
You explain to your boss that the weight of the plants treated with MagicFood is generally higher than the weight of plants which did not receive it.
He answers:
-"Generally higher"? Fine, that means that MagicFood has an effect. This is encouraging; however, I'm interested by the mean weight because the benefit is directly linked to the mean weight.
You understand that Wilcoxon test is not sufficient to conclude about means.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please find a procedure that allows you to conclude about means!->S6.ChooseTest]]
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Significantly normal? This would mean that the observed distributions are significantly identical to a normal distribution?
No: Statistical tests can show significant differences, but never significant similarities.]]
(bg:(hsl:0,1,0.8941,0.6))[[Check again !->S11.Normality]]
(set: $TrInd to $TrInd - 2)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Wow!... Did you properly check your p-value ???]]
(bg:(hsl:0,1,0.8941,0.6))[[Check again !->S11.Normality]]
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Fine ! You show that the distributions of both groups significantly deviate from normality.
Even, you can draw the frequency histograms with hist() function.]]
<img src="MachineRoom/histo.jpg" width=300px height=300px/>
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Controls are in blue, MagicFood are in red.
Your boss is impressed by your skills in R, but he would like that you tells whether the new fertilizer increases the weight means or not.]]
(bg:(hsl:0,1,0.8941,0.6))[[So, it's time to test the difference between weight means->S6.ChooseTest]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[You are puzzled because:
* //You did not check for homoscedasticity//: Some studies using ressampling methods show that it is better to use Welch correction systematically rather than to check homoscedasticity and use the correction only if the test leads you to the conclusion of heteroscedasticity.
* //Shapiro tests showed violations of normality// (or you did not compute them), and you are using a parametric test anyway: Basically, normality is required ''only'' for small samples (i.e. when n<30). For larger samples (here n1=629 and n2=939), the central limit theorem applies and normality is unuseful]]
(bg:(hsl:0,1,0.8941,0.6))[[Everything is clear now for me.->S15.Student]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[If you are still puzzled, please ask to your teacher. He is no more a teacher, he is managing StatiPro, a society specialized in statistical consulting. He will be pleased to send you a proformat invoice with a special price for you, depending on your question.]]
(set: $TrState to "KO")
(set: $StudDF to (prompt: "Please indicate here the degree of freedom of the test Please copy ''(text-colour:yellow)[all digits]''!):", ""))
(set: $StudDF to (num: $StudDF))
(set: $DifDF to $StudDF - 1322.1)
(set: $DifCar to $DifDF * $DifDF)
(set: $DifSDF to $StudDF - 1566)
(set: $DifSCar to $DifSDF * $DifSDF)
(if: $DifCar < 1)[(bg:(hsl:0,1,0.8941,0.6))[[Please click here to validate ->S20.StudSignif]]]
(elseif: $DifSCar < 1)[(bg:(hsl:0,1,0.8941,0.6))[[Please click here to validate->S19.NoWelch]]]
(else:)[(bg:(hsl:0,1,0.8941,0.6))[[Please click here to validate->S18.StudBigError]]]
(set: $BadStud to "ok")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Wow! What did you do? Typing error or more basic problem?]]
[(bg:(hsl:0,1,0.8941,0.6))[[Please try again->S17.StudRes]]]
(set: $TrState to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[According to the p-value, your conclusion is that:]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[We can consider that MagicFood increases significantly the weight of the plants->S22.GoodStud]]]
(bg:transparent)[● [[We cannot consider that MagicFood has an effect on the weight of the plants->S21.BadStud]]]
[● [[We can consider the weight of the plants that were treated whith MagicFood is significantly lower than control plants->S21.BadStud]]]]
(if: $TrState is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Mmmh... Not really bad, but I have the feeling that you don't like the Welch correction.]]
[(bg:(hsl:0,1,0.8941,0.6))[[Please do it again with a Welch correction->S17.StudRes]]]
(set: $TrState to "KO")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Fine! This result is encouraging. Now you have to compare the efficiency of MagicFood with the efficiency of the competing fertilizer.]]
[(bg:(hsl:0,1,0.8941,0.6))[[You need to read the press release again?->S23.PressRelease]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Obviously, the only way to compare the efficiency of the two fertilizers is to use an effect size index.]]
[(bg:(hsl:0,1,0.8941,0.6))[[You will compute the effect size->S24.ES]]]
(if: $TrStateBis is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[There is a mistake somewhere. You gave the true df but your interpretation is wrong.]]
(if: $BadStud is "ok")[]
(elseif: $BadStud is "ReallyBad")[(bg:(hsl:0,1,0.8941,0.6))[Another mistake!
Maybe you should ask to your former teacher. He will send you a proformat invoice with a special price for you, depending on your question.]]
(set: $BadStud to "ReallyBad")
(bg:(hsl:0,1,0.8941,0.6))[[Please give another interpretation->S20.StudSignif]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](text-colour:black)[
Our company is pleased to inform you that we developed the StronGrow, a new fertilizer.
With StronGrow, the weight of harvested plants is significantly increased, and as measured by the Cohen's d (1.05), we can certify that the benefit is large as compared to untreated plants.
Moreover, the number of harvested plants is equivalent to the proportion observed in plants cultivated without fertilizer (about 62%) indicating the absence of toxicity.]
(bg:(hsl:0,1,0.8941,0.6))[[]]
(link-goto: "Return", (history:)'s last)(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Effect size computation is probably new for you. I suggest that you read the article of Wikipedia. You can use it to make a choice.
After, you can load the "effectsize" package. There are other available packages computing effect size (like effsize, pwr...) but with this one, you will find all the effect size index that you need for this challenge.]]
[(bg:(hsl:0,1,0.8941,0.6))[[Let's go for effect size computation->S25.ESComput]]]
[(bg:(hsl:0,1,0.8941,0.6))[[If you need to read the press release again, please click here->S23.PressRelease]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[You could read that effect size indices may belong to 3 famillies. Which kind of effect size will you choose?]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[Correlation family->S26.BadFamily]]]
(bg:transparent)[● [[Difference family->S27.GoodFamily]]]
(bg:transparent)[● [[Categorical family->S26.BadFamily]]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Mmmh... You should not click randomly!]]
(bg:(hsl:0,1,0.8941,0.6))[[Please make another choice->S25.ESComput]]
(set: $TrState to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[You are true : the "difference family" is suited when you need to compare two means.
Among the effect size indices belonging to this family, which one will you choose ?]]
[(bg:(hsl:0,1,0.8941,0.6))[[You need to read the press release again?->S23.PressRelease]]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[Standardized mean difference->S28.BadIndex]]]
(bg:transparent)[● [[Cohen's d->S29.GoodIndex]]]
(bg:transparent)[● [[Glass' Δ->S28.BadIndex]]]
(bg:transparent)[● [[Hedges' g->S28.BadIndex]]]]
(if: $TrState is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Probably, you had good reasons to choose this index. However, in this situation, this is a bad choice.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please choose another effect size index->S27.GoodFamily]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Good choice !
The four proposed indices are good in some ways and it's often difficult to choose between them.
However, in this situation, you are computing effect size in order to compare your results with results obtained previously by another team. Therefore, you ''must'' use the same index as them.]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Now, please compute the Cohen'd (with the //effectsize// library).]]
(bg:(hsl:0,1,0.8941,0.6))[[When you get the Cohen's d value, please click here->S32.Cohen's d]]
(bg:(hsl:0,1,0.8941,0.6))[[R answers something like "Not possible to find the function..."->S30.Library]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[If you don't know which function you should use or how to use it, please read the help of the library or the help of the funcion.
//N.B.: Don't tell that to your teacher or he will ask you for money//.]]
(if: $TrStateBis is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")(set: $Coh to (prompt: "Please indicate here the absolute value of the Cohen's d ''(text-colour:yellow)[all digits]''!):", ""))
(set: $Coh to (num: $Coh))
(set: $DifCoh to $Coh - 1.04)
(set: $DifCohCar to $DifCoh * $DifCoh)
(if: $DifCohCar < 0.0000233)[(bg:(hsl:0,1,0.8941,0.6))[[Good ! Now, you have to interpret your results ->S34.CohOK]]]
(else:)[(bg:(hsl:0,1,0.8941,0.6))[[Please click here to validate->S33.CohBigError]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[The Cohen's d is 1.04. So, what is your feeling ?]]
[(bg:(hsl:0,1,0.8941,0.6))[[You need to read the press release again? (reading newspapers is free)->S23.PressRelease]]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[You are happy because you demonstrate that MagicFood looks better than the other fertilizer->S35.BadInterp]]]
(bg:transparent)[● [[You are a bit desapointed because MagicFood efficiency is about the same as the efficiency of the other fertilizer->S37.GoodInterp]]]
(bg:transparent)[● [[You are a really desapointed because MagicFood efficiency is lower than the efficiency of the other fertilizer->S36.Pessimist]]]]
(if: $TrState is "OK")[(set: $TrInd to $TrInd + 2)]
(if: $TrStateBis is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Wow! What did you do? Typing error or more basic problem ?]]
[(bg:(hsl:0,1,0.8941,0.6))[[Please try again->S32.Cohen's d]]]
(set: $TrStateBis to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[It means that you probably did not install the "//effectsize//" library on your computer or that you forget to load it in your R session.
Please install and/or load it and try again.]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[If you feel unable to install and/or load it, please ask to the consusting teacher. He will be pleased to make money.]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[When the "//effectsize//" library is ready to use on your computer, please compute the Cohen'd and...]](bg:(hsl:0,1,0.8941,0.6))[[...click here !->S32.Cohen's d]]
(set: $TrState to "KO")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[No! You found a Cohen's d of 1.04. The Cohen's d for the other fertilizer is of 1.05 and is therefore a bit higher than yours.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please revise your interpretation! ->S34.CohOK]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrStateTer to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Yes, actually, the two Cohen's d are almost the same. According to the mean weight, your new fertilizer doesn't looks better.
At least, you should check whether the proportion of harvested plants with MagicFood reaches the proportion of plants harvested when they are treated with the competing fertilizer.
Please compute this proportion and compare it with control plants with the appropriate statistical test.]]
(bg:(hsl:0,1,0.8941,0.6))[[Click here when it's done->S38.PropTest]]
(if: $TrStateTer is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")
(set: $TrStateTer to "OK")(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Don't be so pessimistic! The two Cohen's d are not so different... Watch the interpretation scale on Wikipedia and...]]
(bg:(hsl:0,1,0.8941,0.6))[[...revise your interpretation! ->S34.CohOK]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrStateTer to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[According to the press release, we harvest 62% of the plants when they are not treated with fertilizer or when they are treated with the competing fertilizer. Please compare the proportion of harvested plants in your control group to this expected (62%) proportion.]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[Click here when it's done->S39.PropTheo]]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[If you need some help, please ask to your teacher. He will make a special price for you.]]
(set: $BadPropTh to "ok")(set: $PrTh to (prompt: "Please indicate here the p-value of the test ''(text-colour:yellow)[all digits]''!):", ""))
(set: $PrTh to (num: $PrTh))
(set: $DifPrTh to $PrTh - 0.5797)
(set: $DifPrThCar to $DifPrTh * $DifPrTh)
(if: $DifPrThCar < 0.0000001)[(bg:(hsl:0,1,0.8941,0.6))[[Good ! Now, you have to interpret your results ->S41.PropThOK]]]
(else:)[(bg:(hsl:0,1,0.8941,0.6))[[There is a problem. Please click here to identify the problem->S40.PropThBad]]]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Fine, you properly computed the p-value (p=0.58). What is your interpretation?]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[The proportion of harvested plants in your control group is significantly ''lower'' than the proportion generally observed without fertilizer->S42.BadInterp]]]
(bg:transparent)[● [[The proportion of harvested plants in your control group is significantly ''equal'' to the proportion generally observed without fertilizer->S42.BadInterp]]]
(bg:transparent)[● [[The proportion of harvested plants in your control group is ''not'' significantly ''different'' than the proportion generally observed without fertilizer->S43.GoodInterp]]]
(bg:transparent)[● [[The proportion of harvested plants in your control group is significantly greater than the proportion generally observed without fertilizer->S42.BadInterp]]]]
(if: $TrState is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(if: $PrTh < 0)[(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[What?!!! A p-value lower than 0? Where did you learn statistics?]]]
(if: $PrTh > 1)[(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[What?!!! A p-value greater than 1? Where did you learn statistics?]]]
(if: $BadPropTh is "ok")[(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Your p-value looks curious. Did you do a typing error? ]]]
(if: $BadPropTh is "ReallyBad")[(bg:(hsl:0,1,0.8939,0.6))[Another mistake!
Maybe you should ask to your former teacher. He will send you a proformat invoice with a special price for you.]]
(set: $BadPropTh to "ReallyBad")
(bg:(hsl:0,1,0.8941,0.6))[[Please try again->S39.PropTheo]]
(set: $TrState to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[No! You found the true p-value but you failed to give a proper interpretation.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please revise your interpretation! ->S41.PropThOK]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Fine! Actually, the proportion of harvested plants in your control group (62.9%) is not significantly different than the proportion generally observed without fertilizer (about 62%). Therefore, you can consider that your working conditions are about the same as standard conditions (and as the conditions of the study about StronGrow.
Now, you can compare the proportion of harvested plants when they are treated with MagicGrow to the proportion of plants harvested in the control group.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please perform the appropriate test and click here whent it's done->S44.PropObs]]
(if: $TrStateBis is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")
(set: $PrObs to (prompt: "Please indicate here the X-squared of the test ''(text-colour:yellow)[all digits]''!):", ""))
(set: $PrObs to (num: $PrObs))
(set: $TheGood to 281.91)
(set: $DifPrObs to $PrObs - $TheGood)
(set: $DifPrObsCar to $DifPrObs * $DifPrObs)
(if: $DifPrObsCar < 1)[(bg:(hsl:0,1,0.8941,0.6))[[Good ! Now, you have to interpret your results ->S46.PropObsOK]]]
(else:)[(bg:(hsl:0,1,0.8941,0.6))[[There is a problem. Please click here to identify the problem->S45.PropObsBad]]]
(set: $BadPropObs to "ok")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[According to the p-value (p<2.2e-16) and to the observed proportions of harvested plants, your conclusion is that:]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[MagicFood significantly decreases the number of harvested plants->S47.BadPropObsInterp]]]
(bg:transparent)[● [[MagicFood do not significantly changes the number of harvested plants->S47.BadPropObsInterp]]]
[● [[MagicFood significantly increases the number of harvested plants->S48.PropObsInterp]]]]
(if: $TrState is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Wow! What did you do? Typing error or more basic problem ?]]
(if: $BadPropObs is "ReallyBad")[(bg:(hsl:0,1,0.8939,0.6))[Another mistake!
Maybe you should ask to your former teacher. Maybe he will make a special price for you.]]
(set: $BadPropObs to "ReallyBad")
(bg:(hsl:0,1,0.8941,0.6))[[Please try again->S44.PropObs]]
(set: $TrState to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[There is a mistake somewhere. You gave the true df but your interpretation is wrong. Please check the p-value again.]]
(if: $BadPropObsInt is "ok")[]
(elseif: $BadPropObsInt is "ReallyBad")[(bg:(hsl:0,1,0.8941,0.6))[Another mistake!
Maybe you should ask to your former teacher. However, I'm afraid that at this stage, you will have to pay the full price.]]
(set: $BadPropObsInt to "ReallyBad")
(bg:(hsl:0,1,0.8941,0.6))[[Please give another interpretation->S46.PropObsOK]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Congratulations, your interpretation is correct.
Now, you have to present your final report to your boss.
What will be your central message ?]]
(bg:(hsl:48,1,0.7,0.65))[(bg:transparent)[● [[It is not interesting to develop MagicFood because it doesn't increases the weight of plants in an higher maner than StronGrow->S49.BadCl]]]
(bg:transparent)[● [[MagicFood increases the weight of plants in the same maner than StronGrow, but permits to harvest more plants. We should therefore develop it.->S50.Triumph]]]]
(if: $TrStateBis is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[//Updated trust index: $TrInd//]]
(set: $TrState to "OK")
(set: $TrStateBis to "OK")
(set: $TrStateTer to "OK")
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[No! You found a Cohen's d of 1.04. The Cohen's d for the other fertilizer is of 1.05 and is therefore a bit higher than yours.]]
(bg:(hsl:0,1,0.8941,0.6))[[Please revise your interpretation! ->S48.PropObsInterp]]
(set: $TrState to "KO")
(set: $TrStateBis to "KO")
(set: $TrStateTer to "KO")
(set: $TrInd to $TrInd - 1)
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"italic")[Updated trust index: $TrInd]]](bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[Congratulations, it is the end of your stay and you succeded to demonstrate the benefits to develop MagicFood.
It is time to check whether you are invited to sign a permanent contract, a temporary contract, to look for a place in another company, or if the boss allows you to seat near the main back-door of the building for begging.]]
(if: $TrStateTer is "OK")[(set: $TrInd to $TrInd + 2)]
(bg:(hsl:270,0.8039,0.5,0.25))[(bg:transparent)[(text-style:"blink")[//Updated trust index: $TrInd//]]]