I am doing a research about the ethics in pharmaceutical industry. I've chosen 7 branding activities followed by pharmaceutical companies.   I want to study the relationship between the perception of ethics in those activities by doctors and how that might affect their prescription behavior. My hypothesis is that more ethical perception can result into better doctors' response.   I used a likert scale of 5 points to identify both "the perception" and "the response" for each activity.  How can I analyze? What tool can better answer my question? should I analysis each activity separately or is there a tool to consider all of them as a whole?
I have some  gained from survey questions.  In my case they are  responses (Strongly Disagree-Disagree-Neutral-Agree-Strongly Agree).  In my data they are coded as 1-5.  I  don't think means would mean much here, so what basic summary statistics are considered usefull?
How to show that $\det(AB) =\det(A) \det(B)$? Given two square matrices $A$ and $B$, how do you show that $$\det(AB) = \det(A)\det(B)$$ where $\det(\cdot)$ is the determinant of the matrix? The indefinite article "an" is used when the following word starts with a vowel sound. For example one write "an adjective" but "a noun".   However, when an abbreviation is used, should this be based on the expanded meaning, or on the letters of the abbreviation.  Specifically, one writes "a noun phrase". However, here on ell.se, the abbreviation "NP" for 'noun phrase" is commonly used. If this were pronounced by sounding out its letters, as "En-Pee" it would call for "an". If it were read as "noun phrase"  it would call for "a". Should one write "a NP" or "an NP" here on ELL?  I incline to "a NP" and i used that in  just a few minutes ago, but I am not at all sure. When transfering data using TLS the browser and server agree the cipher suite to be used - so for example this could be chosen as AES-128 and is (probably) outside of my control. If I separately encrypt a file using AES-256 and then Alice downloads this via her browser (using AES 128) have I still effectively got AES-256 security?  My reasoning goes like this: even if the AES-128 encryption on the TLS link was broken by Eve then all she would get is the AES-256 encrypted file and she would then have to break that encryption to see the plaintext.  Of course the AES-256 key is sent to Alice over a separate channel. When "etc." is at the end of a phrase, do you place a period after it? Example:     It's all about apples, oranges, bananas, etc.   VS.     It's all about apples, oranges, bananas, etc..   Update  What happens if the abbreviation is inside parentheses, do you place a dot after and before the closing parenthesis?     It's all about fruit (apples, bananas, etc.). So I currently have this issue where my Epson WF-3620DWF can't find the blue and yellow cartridges. (They are official epson ones) and I have a full black cartridge in there. How do I force my printer to ONLY print in black and ignore the cartridge(s) not recognised error? How can I have 2 different mod folders with the new Minecraft launcher? Self-promotion in chat We know from the  that it is accepted only in a limited way in answers and frowned upon if found to be spammy. We know from  that it can be deleted at any time from comments if the comment is not relevant or spammy.  But what about the chat? This leaves chat to be the only legitimate place to promote products or services that the user is affiliated to (albeit in an ad-like way).  What is your opinion? postfix fails to send mail with "fatal: unknown service: smtp/tcp" $X$ is a topological space with no special properties.  If a space $X$ has no isolated points, then show the same for any dense subset of   $X$.  Thanks a lot. I'm a mathematician interested in abstract QFT.  I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal operator.  I understand from the Wikipedia article that requiring that energy stay positive forces $T$ to be represented by an anti-unitary operator.  But I don't see how this forces $T^2=-1$.  (Or maybe it doesn't force it, it merely allows it?)  Here's another version of my question.  There are two distinct double covers of the Lie group $O(n)$ which restrict to the familiar $Spin(n)\to SO(n)$ cover on $SO(n)$; they are called $Pin_+(n)$ and $Pin_-(n)$.  If $R\in O(n)$ is a reflection and $\tilde{R}\in Pin_\pm(n)$ covers $R$, then $\tilde{R}^2 = \pm 1$.  So saying that $T^2=-1$ means we are in $Pin_-$ rather than $Pin_+$.  (I'm assuming Euclidean signature here.)  My question (version 2): Under what circumstances are we forced to use $Pin_-$ rather than $Pin_+$ here?  (I posted a  on physics.stackexchange.com last week, but there were no replies.)    EDIT: Thanks to the half-integer spin hint in the comments below, I was able to do a more effective web search.  If I understand correctly, Kramer's theorem says that for even-dimensional (half integer spin) representations of the Spin group, $T$ must satisfy $T^2=-1$, while for the odd-dimensional representations (integer spin), we have $T^2=1$.  I guess at this point it becomes a straightforward question in representation theory: Given an irreducible representation of $Spin(n)$, we can ask whether it is possible to extend it to $Pin_-(n)$ (or $Pin_+(n)$) so that the lifted reflections $\tilde R$ (e.g. $T$) act as an anti-unitary operator. Make rigid body collide with hair particles Renaming files in lexicographical order with a numerical pattern that increases sequentially with fixed padding I have files such as  a bb ccc abc emrls   I would like to rename them so that, after sorting them (for example, lexicographically), each file gets the following name:  00001 00002 00003 etc   where the # of digits for the 0 padding is specified a priori, e.g. 6 in the case above (assuming that we know how many digits are needed).  Since the shell I am most comfortable with is zsh, I'm interested in solutions that benefit from features on zsh (maybe using zsh's zmv?). I would also be interested in solutions that are compatible with Bash. How to implement a progress bar using the MVVM pattern Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$ Book about space alien cats Consider the following table:  id  title   genre1  genre2  genre3  genre4  genre5 1   Movie1  Thriller    Crime   NULL    NULL    NULL 2   Movie2  Fantasy NULL    NULL    NULL    NULL 3   Movie3  Political   Philosophical   Historical  NULL    NULL 4   Movie4  Science Fiction NULL    NULL    NULL    NULL   When I unpivot genre1, genre2, ... the NULL values are removed, so that, for example, the rows for Movie1 would be:  id title  genre     original_column 1  Movie1 Thriller  genre1 1  Movie1 Crime     genre2   Is there a way to include NULL values, for example:  id title  genre     original_column 1  Movie1 Thriller  genre1 1  Movie1 Crime     genre2 1  Movie1 NULL      genre3 1  Movie1 NULL      genre4 1  Movie1 NULL      genre5   I can SELECT ISNULL(genre1, '*'), ISNULL(genre2, '*') ..., but suppose I want the values to appear as NULL? Is there a better way than:  WITH  -- SELECT that unpivots table AS unpivoted SELECT unpivoted.id,    unpivoted.title,    ,CASE unpivoted.genre WHEN '*' THEN NULL ELSE unpivoted.genre END    ,unpivoted.original_transaction FROM unpivoted   Also, I notice that the query that returns the source data to be unpivoted MUST have an alias. For example:  SELECT ... FROM   -- *must* give it an alias or it's a syntax error   (SELECT ... FROM) AS source    UNPIVOT(genre for original_column IN (genre1,genre2, genre3,genre4,genre5))   Does anyone know why? I have not found a way to refer to the alias anywhere in the query. Proving Invertibility and Eigenvalues If matrix $A$ is an $n\times n$ matrix such that $A^2 -A -2I=0$.  How can I show that $A$ is invertible and that $A^{-1} = \frac12(A-I)$? Also, how do I show that one of the eigenvalues of $A$ is $2$ or $ -1$? I appreciate any help on this question. Indirectly access environment variable Given I have in a bash script  ev=USER   How can I get the environment variable value for $USER using ev?  Tried naively doing:  echo ${"$"$ev}   which results in bad substitution.  I'd expect to get back whatever the value of $USER is. Best way to recover mysql from a "chmod -R 777 /" with databases intact How do I set environment variables from Java?