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Mistake in my experiment
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The most important thing for you to do at viva is acknowledge the error and demonstrate your understanding of it's implications.

I say this as an examiner (with the obvious proviso all examiners are not the same, but having worked with internals/externals I think I have a reasonable feel for the general consensus):

A 'perfect' thesis is not required to get a PhD. There needs to be a contribution to science, but it need not be groundbreaking.

More importantly, as an examiner, you're often asking the question 'is this person sufficiently skilled to be an independent researcher?'. Having made mistakes, realising them, and their implications, is not a bad thing.

The first big mistake you could make would be to attempt to defend flawed work at viva (or, to a lesser extent, be unaware of it). When this happens it's a big cause of difficult discussions when the candidate leaves the room, because someone who's either willing to 'fudge' data/results, or is abundantly naive, is not sufficiently skilled to be an independent researcher. The second big mistake is to defend conclusions data doesn't support - the classic being attempting to generalise to a population from a tiny sample. Often candidates worry too much on the 'need for a contribution' side and end up trying to defend a contribution their data doesn't support. Corrections issued are often about toning down the conclusions in this regard - because it's dangerous/damaging in academia to claim things that aren't proven.

Don't be 'might have' affected the results, be 'x study showed.... influence of this form of surveying'. The most important thing at viva in terms of outcome (to the limited degree you can influence it at that stage) is to be knowledgeable, confident, honest, and speaking like an academic, rather than someone desperately trying to fake it through a test.

Got requested to terminate my studies?
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In general, these decisions are made (or supposed to be made) with the student's best interests in mind.

If you didn't get up to speed on the background etc., the difficult decision for the University/panel is whether it's in your best interests to continue to study (and potentially pay) without a likely completion. If, based on progress to date, their consensus is you'd waste even more effort in a failed or never-submitted PhD, then it makes sense to terminate it for everyone involved.

You should appeal if you think you can genuinely put in the effort to solve the problems. If circumstances have changed and this is going to be the case, then you should appeal and state this case.

Your personal circumstances typically need to be formally reported to the University to 'count'. Many, many PhD students fail to do so because you can be in bed sick/depressed/bereaved etc. and still 'work' on a PhD (because you're not usually expected to be sat at a desk 9-5), which leads them to attempt to 'work through' these situations - then they are inevitably penalised because they've not formally been away. If you do take the route of appealing and continuing, and circumstances change again, I would make sure you approach it as though you had a 9-5 job and take formal leave of absence.

Viva Questions...
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General questions usually mean either:

1) It's the start of the viva, and the examiners are trying to de-stress you a bit by giving you some easy questions which you googled in advance and can knock out of the park.

2) It's the end of the viva, it's gone well, and they're genuinely interested in your future plans, and how they could support.

There are really no right answers to these questions, in the sense of them meaningfully affecting the viva outcome, unless you really shoot yourself in the foot ('I definitely evolved as a researcher because I realised I could fake data and get away with it!').

The traps on the questions you list, broadly speaking, are:

- How has your view of the area changed? Trap: if it hasn't, you've learned nothing and found nothing out.

- What problems did you have? Trap: If no problems, is your thesis 100% flawless on this, or are you being naive?

- How have you changed? Trap: I am exactly the same as I was when I started with a Masters, but expect a PhD now. Explain what you have learned.

- What surprised you? Trap: If nothing you discovered was scientifically unknown or unexpected, how is this research? Think of surprised not in the literal 'gasp' sense, but in the 'I found something new out' sense.

- What would you do differently? See 'What problems did you have'. Trap: Attempting to argue your PhD is completely flawless. Slightly flawed with awareness of flaws is a PhD; Flaws with a complete lack of awareness of these flaws is a possible fail.

Part time and funding - advice needed
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1) I would not personally recommend a distance learning PhD, because they sound a bit like cash-grab teaching for minimal effort on the (virtual) supervisor's part. It perhaps depends on why you want to do it; if it's for a job in research afterwards, you'll need to make connections, which will be incredibly hard if your actual contact with the research community is a bi-monthly skype call. You will be paying a lot of money, so the support, and more importantly the opportunities to network, are something to evaluate.

2&3) Basically; in the UK, academics apply for funding from councils/trusts/companies/whatever moves, not students. If an academic is successful and has nobody lined up (hence the importance of networking opportunities as per 1), then they will tend to advertise a paid studentship on jobs.ac.uk. This will rarely be part-time though. Universities also invest directly in studentships, however, they're usually full time because, cynically, for the Uni the purpose of the investment is to get on-time (3 year) completions for league tables.

4) It is worth noting it is very rare for a student that starts self-funded to get offered funding down the line. Perhaps the odd 'extra work' opportunity (e.g. teaching), but because most funded opportunities are linked to projects that start and end in a PhD lifecycle, you can't move onto one halfway through easily.

5) If you are self-funding I would firmly consider yourself the customer at the application stage (though, not necessarily at the supervision stage, as your supervisor will be doing it for the teaching/research, not the income, which will go straight to a nebulous university pot). I would consider: whether there's a substantial active team researching what you're doing; the track record of the potential supervisor(s); whether there are active related projects within the group; whether there are other PhD students; & the ranking of the University.

Hope this helps.

possible outcomes of minor corrections
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I say it can't be bounced because I asked, as examiner for a UK university, when a corrected thesis landed on my desk with the corrections done very poorly (or not at all in some cases).

This put me in a position of either failing a PhD completely because of minor issues, or effectively passing it still with minor issues.

I passed it, because it seemed the considerably lesser of two evils. I'd think most examiners would lean the same way. Nobody wants to take 3+ years of someone's work and throw it in the bin, unless it's patently damaging to academia if they don't (e.g. it's faked data, completely nonsensical, zero contribution, dangerously misleading conclusions, etc.).

This is not a bad policy per se, as the alternative could lead to worst-case scenarios where corrections end up as an endless and increasingly subjective back-and-forth.

The student doesn't 'win' in that scenario, though, because they're then going to go on and publish a thesis with errors, which may haunt them for the rest of their career. Really, at the point of submitting corrections, if you feel happy to have it published with your name on as (probably) the only PhD you'll ever do, and as the culmination of 3+ years of work, you're probably in the right place.

possible outcomes of minor corrections
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Corrections in most (possibly all) UK universities cannot be 'bounced back'; they're a pass or fail.

In a way the advice above about 'genuine effort' is true but should be taken with caution. From an examiner's perspective, they've seen a thesis that was more-or-less-ok, but needed correcting. If you put yourself in their shoes - would you then fail a student's 3+ years of work because there was still a typo?

That said; if the typo is in the title of the thesis and there's a general vibe of 'I completely ignored all the feedback you gave me after volunteering the time to carefully examine my thesis', there is an obvious risk there. Yet of course this seldom happens, because most students will spend the time to address the corrections rather than take this risk.

In my experience in UK academia it's untrue that only the internal reviews minor corrections though I'm sure there may well be Universities where this is the case.

PhD Fellowship is lower than I was told
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Do always ask.

Your supervisor (or any academic in general) will usually support students in getting the best stipend they can. Often it falls off their radar if the student never raises it; it's not them actively blocking you getting more money, it's just that they're not aware. It's not greedy, ungrateful, or inappropriate to ask for a higher stipend. It may or may not be possible, but if you don't politely ask, and gently push, it will not happen.

Regarding Marie Curie ITNs, as you probably know the reason they offer a higher salary/stipend is they require international (and usually intersectoral) mobility, so they're in effect providing researchers with a financial incentive to do something they wouldn't otherwise want to do. This can work fantastically in some cases (usually where everybody knows each other beforehand); but can be an absolute disaster in others, so if you felt it wasn't right for you, you very probably made the right decision.

At what stage do you approach potential supervisors?
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If you are self-funded, you will probably find many doors are open.

The best advice I could give would be to treat the whole process as a two-way interview. You don't need to be too afraid of rejection or sending a bad proposal, what you do need to worry about is paying a small fortune for a supervisor that doesn't engage with you leading to a drawn out, isolated part-time PhD.

That said - strategically - consider sending the proposal to a few places that you're the least interested in first. If you get no answer or negative feedback (or even positive suggestions), you can take this onboard before sending it to the places you're most interested in.

Examiners judging my research on the wrong elements?
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It's a bit worrying to see CS and maths viewed as completely different things. I'd think - perhaps optimistically - what they're trying to nudge you towards is a good PhD with a robust theoretical grounding, and to achieve and communicate this without a reasonable grasp of the core bits of maths would be nigh-impossible.

It is a very common problem in CS that PhDs can tend to focus on what's hard, rather than what's research (research is a subset of hard!). It's very easy in computer science to spend a lot of time programming something that's complex, but this doesn't automatically mean it's research - and the trap there is you can feel like you're doing something worthwhile because it's hard and time consuming, rather than because it's good science.

This goes double if you're working with a company, because they can sometimes tend to focus and feed-back based on what they need - a practical solution - rather than what it contributes to science - a PhD.

The good news is you're still at an early stage and can consider and react. As an internal review, there is typically little to be gained from complaining about or contesting the process if the result is a 'pass but do some extra work on this' (much easier and more productive to do the work than go through a complaint process). I would instead try to clarify why they feel it's relevant to your research, and approach that discussion very open-mindedly.

Dissertation Partner being published but not me-same data
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There are no generic rules about publication credit in academia, only general perceptions of what is/isn't cool (which varies between groups, institutions, and disciplines).

It sounds like you had a significant role in the work related to the potential output. Author credit to me would seem appropriate. This is probably an introduction to politics, in academia. In my experience, navigate as follows...

1) Are you sure you're being excluded from the output, as you're working forwards from a worst case scenario, it seems. Unless barriers are being put up I would just speak to the colleague and supervisor in terms of 'so I heard there's a plan to publish the data I helped collect? Just let me know what I can input to the paper' (and input your name as a co-author while you do it!) as this is a) helpful and b) not needlessly confrontational. Possibly do this with the supervisor first as they're far less likely to be massively invested in it, and your colleague is likely to follow their direction.

2) If it seems like they want to deliberately exclude you or incredibly pent-up on who co-authors what, then either a) they're jerks, and are needlessly burning bridges on the basis that having 1 additional author on a paper will meaningfully impact their careers; or b) there's a consensus you didn't meaningfully contribute and are trying to leech credit. In either case, you'd need to consider then confront and state your case very carefully.

Folks can probably advise in more detail on 2) but I'd really make sure 1) isn't the case first.

Apply for a PhD when already enrolled
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Yes, you *can* but I'd think carefully about:

a) Can you shape the current PhD to be what you want to do? If not, why not? If it's that is has restrictive funding requirements - and you're happy to give these up - it would be a good reason. If it's something more nebulous (don't *think* prof would let you do it), be careful these are certainties rather than assumptions before proceeding.

b) Accept that a PhD is often monotonous, repetitive, hard work. This is not a 'bad' PhD, it's often the nature of research. Switching topic will not magically fix this - you'll just realise the thing you thought was interesting is also monotonous, repetitive, hard work to investigate rigorously. Of course, this is a cynical perspective - the ideal situation is you're down the pub on a Friday explaining why what sounds as boring as hell to everyone else is super-interesting - because you're finding the monotonous, repetitive, hard work compelling.

c) It would be up to you, I'd presume, whether you disclose that you're currently doing a PhD elsewhere. As a supervisor I'd rather someone be up-front and explain why they want to switch - and be trying to assess if a) or b) above apply. I'd try to answer these questions to yourself, convincingly, so you can be up front and make the same convincing argument on the application, or rethink things.

Proof of my masters?
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A scan of the certificate would be what I'd expect, if I asked for it.

You'd possibly want to bring the certificates to the interview, if this is relevant to your situation. Generally this is more for HRs benefit than the interviewers' - by which I mean, these policies/processes are typically driven by HR rules (which themselves are designed to catch rare/ridiculous 'worst case' scenarios) rather than a burning passion from the professor doing the interview to see a candidate's life history in print, signed in triplicate!

In short - send a quick scan; if they're not happy with it they'll let you know what they do want, and either way it shouldn't affect your chances.

What is a double-baseline design?
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Treatment is started & baselined at different times. Because there are two baselines, we can attempt to infer the treatment is the cause of the effect. This assumes a hypothesis that the treatment's benefit is exposure time related (a reasonable assumption in most forms of behavioural intervention).

e.g. - You do the same depression intervention on two cohorts, which start 1 month apart. You baseline both at start point for respective cohort. Both cohorts report monthly depression-inventory scales. Cohort 1's response markedly improves vs their baseline 3 months later. Cohort 2's markedly improves vs their baseline 4 months later, with them having started the intervention a month later. The fact both baselines improved within a similar duration of exposure to the intervention supports the hypothesis the intervention is the causal factor.

Benefit - all participants are exposed to intervention. This can be important both ethically and pragmatically. But the same could sometimes be achieved with a crossover design.

Drawback - you may still fail to accommodate extraneous factors. For example, if both interventions are led by the same facilitator - is it the content of the intervention, or the skill of the facilitator? Similarly, depending on the temporal aspect, and the power of your stats, something extraneous could still happen in week 2.5 (like a TV documentary on depression), with sufficiently strong an effect to influence both sets of responses.

urgent question
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Presumably there was a rationale for doing both. I would imagine the interviews were there to provide qualitative insight to support or refute the quantitative data.

Whether this is needed, useless, or can be omitted depends very much on your hypothesis and research design. If your survey metric has been validated though other correlations, is well-designed, and has a sample appropriate for your analysis techniques (i.e. is not a fudged ANOVA of 30 Likert responses), then it may stand alone as a contribution worthy of a PhD. Similarly you can build a PhD purely on qualitative work but will have to defend other questions such as how representative the sample is, and how findings might generalise.

Surely if you have the data, a survey would be quick to analyse (though, admittedly, if you have 1,000 hand-filled papers rather than a SurveyMonkey report I'd see the problem). Since you've already undertaken the qualitative work, then if time really is an issue an option might be to pick several interviews as detailed case studies rather than report them all? If transcription is the problem then see if you have budget as a student to pay for this using a service.