MathHelp

I'm really confused by why inclusive disjunctive can also include both parts being true. I have been googling explanation and reading books on it but to be honest the explanations don't make a lot of sense to me - it is almost like they assert something that seems obviously wrong and then move on. How can it be that when I say "you are either good at hockey or bad at hockey" that it could also be that I am both good and bad at the same time? What if someone likes dogs so I use the addition rule of inference and reason: Greg likes dogs. Therefore either Greg likes dogs or he likes cats. Even though it may be that Greg likes both cats and dogs, I know that logic asserts that this is a correct deduction because logic treats "either... or..." as meaning both or/and but how can that be true in reality? I don't know how else to explain my confusion but I am hoping the confusion is something everyone else has gone through at some time. It is like saying "ships can fly" and then declaring the statement to be true because "flying also means floating" (when it obviously doesn't).

Thanks, that makes perfect sense to me according to my understanding of null and alternate hypothesis. But I am still confused by studiot saying I have not formalised the null hypothesis correct - can you see any errors???

Oh, but I learned that from a textbook. Can you tell me what is wrong with it and what the correct formulation would be?

Apologies, I didn't understand your response. Hypothetical reasoning is a form of induction (not deduction). A hypothesis is used to explain an event or to help conceptualize something. Induction: premises suggest the conclusion is true (but it could be wrong). Deduction: the premises imply the certainty of the conclusion (assuming the premises are true). I understand that later on in the scientific process that deduction would be used when looking for implications of the hypothesis - but that is not related to what a hypothesis is/is not. What I am wanting to know is how do philosophers/logicians incorporate null/alternate hypothesises into there ideas about what a hypothesis is and how they work. That's the key right there - I am not wanting to know where adequacy, consistency, fruitfulness etc etc fit within chemistry (the coolest science)or statistics. I want to know where null hypothesis and alternate hypothesis fit within philosophy. It's a philosophy question. Thanks for your response though.

Hi team, It is common for a hypothesis to be described as an "explanation" for something or an event. But in statistics we use: Null hypothesis: Population characteristic = observed characteristic. Alternate hypothesis 1: Population characteristic [greater than] observed characteristic. Alternate hypothesis 2: Population characteristic [less than] observed characteristic. Alternate hypothesis 3: Population characteristic [not equal to] observed characteristic. A statistic study is conducted in order to obtain evidence/proof for an alternate hypothesis. If enough evidence/proof is found is support of an alternate hypothesis then the null hypothesis can be rejected in favour of it. But these hypothesises don't seem to offer explanations. They can also hardly be judged using the criteria of adequacy, internal consistency, external consistency, and fruitfulness. Any input is welcome...

I studied logic many years ago and I don't recall learning anything related to arguments from signs. My recollection is just that there was a chapter in a book that listed the different types of inductive arguments (generalisations, probability, analogies, signs etc etc). There were techniques/methods for making different types of arguments but I don't recall there being anything about arguments from signs. Any suggestions? Or is the only thing you can do with an argument based on signs is to simply identify it as such an argument and then move on.

Hi team, So the addition rule of implication is as follows: P therefore either P or Q. Apparently, this is a logical implication because if you know P to be true then the overall statement "either P or Q" will always be true. However, what if it was actually P and Q? As an example: I like cats (P). The addition rule of implication says that the following proposition must be true: Either I like cats(P) or I like dogs(q). But I actually like cats(P) and dogs (q). Doesn't that mean the rule can lead to errors?

Hi team, I studies statistics in my first year of Chemistry study. That was many years ago but I found it to be an amazing topic. I would like to learn more about statistics. Presumably what people would learn if they did a second or third year course in statistics but I don't know where to find study material. What kind of textbook would teach me slightly more advanced statistics. I already know the basics of descriptive statistics as well as T tests, Z tests, Chi squad, regression, and ANOVA. As an example, I would like to learn how to do a meta-analysis. I got a book on Biostatistics and it seems to have a little bit of new content like geometric and harmonic means as well as discussions of case control and cohort studies. I work full time and am not in a position to do formal study so this would just be for study in my own time.

I am looking for a good game that I can play on a daily basis to improve my basic medical knowledge as part of studying paramedicine. It would be really cool if there was some game like Wordle where you just play it for 1-2 minutes once a day. Obviously I would do more study than this but I think a small game is a good way to retain knowledge after you have completed a course and are studying the next course - that extra 1-2 minutes refresh can really add up over a year.

Hi team, I was wondering how to determine whether a helicopter is good. As an example, with an Army tank, you would judge it on the criteria of protection, firepower, sensors, and mobility. Are there specific things that you can look at to determine that a particular type of helicopter is going to be "better" than others? I am mostly thinking in a military context. I am particularly interested in comparisons between a Blackhawk/NH-90/Mi8 helicopter.

No, sorry I did not see any suggestions to try... or did you mean the triangle/rectangle calculation? The main issue I am having is recognising where it is useful. You have essentially answered this question by giving interest rate and population growth examples. However, I am now curious about when it might be useful for comparing the area of a rectangle with a square. Is that something a Civil Engineer would need to know? A final point of clarification, can someone explain why it is called the geometric mean when it does not seem to have anything in common with the arithmatic mean? As an example, the arithmatic mean is clearly a measure of central tendency - I can intuitively understand what it is trying to tell me about the central tendency of data. Based on the explanations given of the geometric mean, I can understand how it could be used... but it does not seem to have anything to do with central tendency. It can help me estimate the rate of population growth, but that is about estimating and is not related to central tendency. Is the geometric mean relevant in medicine?

I am not wanting to learn calculus for statistics. I am wanting to use statistics as a goal to help me learn calculus. So while I don't need calculus to understand statistics, my final goal is to have a good understanding of calculus. I already know the fundamentals of statistics so just want to use that as something to attach new memories to - learn calculus with a context if that makes sense. Thanks for both your replies.

Thanks for your response. The trouble I am having is understanding what the geometric mean can tell me that is useful. You gave a definition: But why would that be useful to anyone? You mentioned it would be useful in finance and population growth studies but I still can't see what meaningful information it would give to someone. In my head it is like working out a way to calculate the number of branches on the third tree to the right in a hedge of trees. I know how to do it, I can do it, and I know what the answer would tell me (the number of branches on the tree) but I am not sure what insight this would offer... any help on this? Can you give me an example of a real-life problem where the geometric mean would offer someone meaningful insight into a data set and what that meaningful insight would be?

Hi there, I wanted to learn some calculus for statistics but it seems like pre-calculus will take many months. If you look at this page from Khan Academy, it does not look like it will be something I can understand for a long time: Precalculus | Math | Khan Academy I was wondering if the path to calculus would be shorter if there is something very specific I want to achieve. What I would like to do is learn one aspect of statistics through calculus - would anyone be able to offer me a roadmap for that? You can choose the part of statistics that the roadmap applies to. My overall goal is to have a very strong understanding of statistics and eventually understand calculus through statistics. This roadmap would just be a start - I would continue to learn calculus. I happen to find statistics to be a strong motivator for me as I can easily see the direct application to it in my life. Any help would be appreciated. Edit: I'm referring to basic 1st year statistics. Although I am not formally enrolled in a course. I work fulltime and just study a statistics book in my sparetime.

This is all good stuff, it is going to make understanding a lot of other maths ideas a whole lot easier. I always new 22 was 4 and how to calculate exponents, I just never understood how it made sense (I have come across many bad definitions). Because the definitions never made sense, it also meant things like logarithms and square roots never made sense to me either.

That makes perfect sense. Thank you so much!

So I read that the geometric mean is a good indicator of central tendency when data is in logarithmic form. But to me, it would seem that this is a contradiction. Doesn't logarithmic data inherently not have central tendency? I should clarify that my understanding of "logarithmic" is that it means that changes are exponential. So if I have a data set of 1, 10, and 100, how could a geometric mean give me any useful data about the central tendency of this data set? There does not seem to be a central tendency....

Hi team, I'm really struggling with understanding how exponents make sense. According to a basic google definition: "An exponent refers to the number of times a number is multiplied by itself." This would indicate to me that 2 to the power of one would mean that 2 needs to be multiplied by itself... once. So 2 x 2 is 4. But I know that 2 to the power of 1 is actually one. Why is 2 squared not 2x2x2? I can only see two "x"s in there... Thanks for your advice.