Film Review: Star Wars The Last Jedi

I loved it.

My first impressions from the first few minutes was that this was a retread of Empire Strikes Back.  The First Order have tracked down the resistance base on a remote planet, and the resistance are trying to evacuate before the First Order land troops and... oh, wait a minute, there is no shield, no cannon and the base is going to be obliterated from space.  And things seem to go well for the resistance, as they are able to stall long enough to get almost everybody safely aboard their cruiser and off to safety.  But not before Poe Dameron (X-Wing ace turned hot-headed insubordinate comedian pilot) decides to sacrifice the entire bomber fleet just to destroy a Dreadnaught.  Let's here it for Pyrrhic victories!

Worse still, the First Order have developed a way to track the Resistance through hyperspace: running away is not a way to escape, and hyperspace fuel is in limited supply.

At the end of the previous film, Rey had successfully tracked down Luke Skywalker, and much of this film covers her efforts to persuade him to join the Resistance.  So, we have space battles interspersed with the story of a Jedi master and a young Jedi-wannabe/trainee on a remote, green, damp planet.  Like I said, I kept recalling Empire Strikes Back throughout this film. I haven't looked online to see if anybody has listed all the parallels between The Last Jedi and The Empire Strikes back, but I saw a few (and I'm only a casual movie-goer).  Luke Skywalker has traded his youthful naivety and enthusiasm for jaded cynicism.  The way he casually lobs his lightsabre over his shoulder is both funny and tragic at the same time.

My only niggle with the film is the amount of time spent on the story with Rey and Luke.  The other storylines were far more exciting and just downright interesting; Luke and Rey - less so.  Luke goes for a walk.  Luke catches a fish.  Luke wanders around his island.  Yawn.

The plot makes a lot of sense, and there's a direct causal link between the Admiral and her tight-lipped need-to-know authoritarian attitude, conflicting with Poe Dameron's "we have a right to know what's going on" and the subsequent demise of the resistance fleet.  If she'd told Poe what her plan was, he wouldn't have sent Finn off to find the code breaker, who wouldn't have subsequently told the First Order about the resistance's plans and their cloaking frequency (or whatever it was).  If they'd all stayed home, sat tight and waited it out, they might all have survived.  I'm not blaming him or her, but it seems like the two characters managed to deliberately out-hard-head each other - aiming to be the most stubborn character and the one who wins, until neither of them do.

Some of my favourite aspects of the film is how the script addresses some of the criticisms that were levelled at the first of the new films (The Force Awakens).

"Finn should have had that fight with Captain Phasma, not with some random stormtrooper with a cool elbow mounted weapon."  Cue large-scale, violent, hand-to-hand fight between Finn and Phasma.

"Snoke is too much like the Emperor and there's no real explanation for him."  Kill him off - now who saw that coming?

"More Poe Dameron!" - definitely fixed in this episode.  He kicks off the action at the start; we see more of his character throughout this film (borderline arrogant, but still funny) and he commits mutiny.  This is not a replacement for Han Solo; this is a whole new character who has his own ideas, opinions and history.

"Do something different!"  - I saw most of the parallels between The Force Awakens and A New Hope.  In fact, it felt like a rehash of the story with new faces. As I mentioned earlier, The Last Jedi has elements of The Empire Strikes Back in it, but those elements have been rearranged to produce a fresh story (and no, I didn't for one second think "It's salt!", I knew full well it was meant to be snow).

All-in-all, I'm excited for the next installment; I'm looking forwards to the Han Solo movie and I feel even more optimistic for the future of the Star Wars saga.

Mathematically Explaining Confidence and Levels of Significance

Level of Significance: a more mathematical discussion

In mathematical terms, and according to "A Dictionary of Statistical Terms, by E H C Marriott, published for the International Statistical Institute by Longman Scientific and Technical":

"Many statistical tests of hypotheses depend on the use of the probability distributions of a statistic t chosen for the purpose of the particular test. When the hypothesis is true this distribution has a known form, at least approximately, and the probability Pr(t≥ti) or Pr(t≥t0), and Pr(t ≤ ti) and Pr(t ≤ t0) are called levels of significance and are usually expressed as percentages, e.g. 5 per cent.  The actual values are, of course, arbitrary, but popular values are 5, 1 and 0.1 per cent."

In English: we assume that the probability of a particular event happening (e.g. a particular recipe persuading a customer to convert and complete a purchase) can be modelled using the Normal Distribution.  We assume that the average conversion rate (e.g. 15%) represents the recipe's typical conversion rate, and the chances of the recipe driving a higher conversion rate can be calculated using some complex but manageable maths.  

More data, more traffic and more orders gives us the ability to state our average conversion rate with greater probability.  As we obtain more data, our overall data set is less prone to skewing (being affected by one or two anomalous data points).  The 'spread' of our curve - the degree of variability - decreases; in mathematical terms, the standard deviation of our data decreases.  The standard deviation is a measure of how spread out our data is, and this takes into account how many data points we have, and how much they vary from the average.  More data generally means a lower standard deviation (and that's why we like to have more traffic to achieve confidence).

When we run a test between two recipes, we are comparing their average conversion rate (and other metrics), and how likely it is that one conversion rate is actually better than the other.  In order to achieve this, we want to look at where the two conversion rates compare on their normal distribution curves.

In the diagram above, the conversion rate for Recipe B (green) is over one standard deviation from the mean - it's closer to two standard deviations.  We can use spreadsheets or data tables (remember those?) to translate the number of standard deviations into a probability:  how likely is it that the conversion rate for Recipe B is going to be consistently higher than Recipe A.  This will give us a confidence level.  It depends on the difference between the two (Y% compared to X%) and how many standard deviations this is (how much spread there is in the two data sets, which is dependent on how many orders and visitors we've received.

Most optimisation tools will carry out the calculation on number of orders and visitors, and comparision between the two recipes as part of their in-built capabilities (it's possible to do it with a spreadsheet, but it's a bit laborious).

The fundamentals are:

- we model the performance (conversion rate) of each recipe using the normal distribution (this tells us how likely it is that the actual performance for the recipe will vary around the reported average).
- we calculate the distance between conversion rates for two recipes, and how many standard deviations there are between the two.
- we translate the number of standard deviations into a percentage probability, which is the confidence level that one recipe is actually outperforming the other.

Revisiting our original definition:Many statistical tests of hypotheses depend on the use of the probability distributions of a statistic t chosen for the purpose of the particular test

...and we typically use the Normal Distribution When the hypothesis is true this distribution has a known form, at least approximately, and the probability Pr(t≥ti) or Pr(t≥t0), and Pr(t ≤ ti) and Pr(t ≤ t0) are called levels of significance and are usually expressed as percentages, e.g. 5 per cent.

In our example, the probabilities ti and t0 are the probabilities that the test recipe outperforms the control recipe.  It equates to the proportion of the total curve which is shaded:

You can see here that almost 95% of the area under the Recipe A curve has been shaded, there is only the small amount between t1 and t0 which is not shaded (approx 5%).  Hence we can say with confidence that Recipe B is better than Recipe A.

Thus, for example, the expression "t falls above the 5 per cent level of significance" means that the observed value of t is greater than t1 where the probability of all values greater than t1 is 0.05; t1 is called the upper 5 per cent significance point, and similarly for the lower significance point t0."

As I said, most of the heavy maths lifting can be done either by the testing tool or a spreadsheet, but I hope this article has helped to clarify what confidence means mathematically, and (importantly) how it depends on the sample size (since this improves the accuracy of the overall data and reduces the standard deviation, which, in turn, enables to us to quote smaller differences with higher confidence).

New Year's Resolution - Don't moan, complain.

One of my New Year's Resolution's for 2018 is this: don't moan, complain.

What's the difference?

We're very good, as a society, at moaning. Social media has made it even easier to bend our friends' ears about the latest irritation that we've had to suffer: long queues; poor service; sub-standard goods; cold food; inept staff; rude checkout assistants... the list goes on. And we think that sharing our dreadful experience with our friends will avenge us on the service provider - we "warn" our friends against giving their money to the same company and encourage them to support their competitors instead.

That is not complaining; that's moaning.

Moaning: telling everyone about a terrible experience - except the people who (1) caused your inconvenience and/or (2) are in a position to fix your situation or provide redress.  

Complaining: approaching the person who provided the poor service; the lousy product; the long wait or the cold food, and asking them to please fix it.

I don't tend to complain - I think it's rude; I don't want to cause a scene; I don't want to be an inconvenience; I think should just tolerate it and make it a character-building opportunity.

However, I think it's time to make a change, and - when necessary  - to complain instead of biting my tongue (I'd like to think I don't moan much, but the principle is the same). Some stores, cinemas and so on ask for feedback - some shops will enter you for a prize draw if you do - which is a good place to start, but how about this: if you think you're going to go home and then tomorrow tell your friends how bad this place/shop/meal was today, why not tell the staff today? Or at least contact their complaints department so that they can actually do something about it. Make a difference, so that they can make a difference too.