Are there any fabulous statisticians/mathematicians among us?

[Holdingmynerve]

I have a problem to solve and don't really know where to start.

I have a monthly rota which lists all the staff at work on each day. I have reduced this down to their grades. So for example: 50A, 25B, 10C, 2D.

The next day I could have 40A, 30B, 5C, 2D.

I have a months worth of this data.

I also have how the team performed that day - target of 90%. So this is shown as a percentage for the day. However.....I also have the amount of clients that called/visited that day.

So three lots of data. Mix of staff/performance/client numbers.

I would like (if this is even possible) to work out which mix of staff = higher performance and which mix of staff doesn't work so well.

Is this something which would be possible at all? I can't even think where to start, I'm having a complete mental block!

Thanks

@DadDadDad can probably help. I'll pass on this as I never liked mucking around with data.

I should have thought this was a relatively easy calculation.
What industry do you work in?

Could you just workout turnover per client to see which days were best, e.g. £15/client vs £5/client. Then see who you had working on the best and worst days to see if there is any correlation.

[cracks knuckles]

Right, sounds like linear regression might work. Target % is your dependent variable. Each grade of staff (a, b, c, d) is a predictor and gets its own column. Every day is a row, with the numbers of staff per grade and the achieved %.

You'll get back a regression equation that weights each grade of staff according to how it contributes to % achieved. You can mess around with different numbers of staff per grade (within the constraints of your business) to find out what combination results in highest %.

Is the number of clients per day random? If so, you can enter it as a random variable - it would complicate the analysis a bit but give you a more accurate equation.

I appeared to have been summoned.

It sounds like geeka knows what's she's talking about. (I suppose the next stage would be a generalised linear model with cross-terms between the independent variables).

But I always feel like it's worth first just getting your own feel for what might be happening in the data. For example, if you do a scatterplot of performance against clients, does that show any pattern? That might tell you that you are going to have make some adjustment for the number of clients before concluding that a particular team composition is better. What about if you plot performance against the total number of staff, or against the % of band A staff?

This is why I love MN, truly

I'm just off to google 'linear' and 'regression'

The problem is that our outcomes aren't financial, we provide a service and our performance =90% is how well we provide it.

@geekaMaxima, i'm in AWE
@DadDadDad, that was my first thought, I've broken down each day into groups of staff and plotted against performance that day but it really is so dependable on how many clients they have to deal with on any given day.

I set out a very basic line chart which plots performance against number of clients expecting to see low numbers of clients = high performance, high numbers = low performance. But it doesn't show that at all, which leads me to believe its the skill mix of the staff which is possibly affecting the performance stats?

What about a plot of performance v % of staff who are band A? Then repeat for band B etc. Also, doesn't the total number of staff make a difference - more staff, higher performance? The other quick thing you could do is sort the data by performance rating and see if anything jumps out.

@DadDadDad, 'doesn't the total number of staff make a difference' - you'd think so wouldn't you! But again it doesn't follow the logic.

I've tested for total number of staff (it only usually fluctuates by 20/30), no pattern emerges.

I working from the vague idea that a C/D heavy rota works better than any other but that is just a feeling.

I'll try and plot performance against each group and let you know! Thanks for the help

Bumping because this stuff fascinates and horrifies me at the same time

So what differs each day (that you hold data for) is:
-total number of staff
-proportion of staff at each grade
-number of clients
-performance.

You say there appears to be no obvious relationship between total staff and performance, or between number of clients and performance.

Have you looked at the ratio of staff to clients and compared that to performance?

So divide number of clients by number of staff, then plot the result against performance?

Just to be clear, you need the mix of grades, a b c d that were assigned that day? 50a means 50 people of grade a, not Mary, the 50th employee in grade a.

If so, I would start with a liner regression that looks something like
Performance rating = #a + #b + #c + #d + customers served + (maybe some other factors)

For other factors I would consider looking at day of the week, relationship to payday, big sale happening, or whatever makes sense in your industry.

Alternatively, if you have enough data, you might run it separately for day of the week or sale days or whatever makes sense because your ideal mix may be easier to see that way.

But this assumes that all interactions are equal and they may not be. If (say) OP is the NHS and interactions on day one are coughs and colds while interactions on day two are open heart surgeries I would expect the team on day two to look a lot less productive. Not because they are, but because open heart surgery takes a lot longer and involves many more people. So it is also worth checking the types of client contact we are talking about here.

Thanks for something to think about to make the late pregnancy insomnia less dull!

Agree with the previous replies re making sure you’ve thoroughly explored your raw data, and also re the assumption that all your client interactions are equivalent.

For the specific question “does the staff mix affect the performance” I would do the following:

1. Come up with one performance measure: assuming the ideal is to have a lot of client interactions with high performance, taking into account that you have different numbers of staff working then for each day I would calculate (performance %)*(# interactions)/(# staff).

1. Come up with a single figure that reflects your staff mix. You need to assign a value to each grade that reflects their seniority. Assuming that salaries within a banding are relatively similar then an average salary for the band might be a good proxy, else you could simply say that band A = 1 points, B = 2 points, C = 3 points etc (assuming that A are your basic workers and C/D higher level management). If in fact there’s a big jump between being B and C for example you could weight this to make C/D more “expensive”, which is why it might be better to use salaries - let’s pretend that A = 10,000; B = 15,000; C = 25,000 and D = 50,000. Then for the day 50A, 30B, 10C, 2D (for example) you’d do:

(5010,000 + 3015,000 + 1025,000 + 250,000)/(50+30+10+2). On days where you have a higher proportion of C/D, this figure will be higher than a day when you have mostly A/Bs working.

1. Plot the two variables (1. on y axis and 2. on x axis) and see whether it shows that your performance measure (1) is higher on days when the ‘staff seniority ratio’ (2) is higher.

Caveat: when you manipulate data like this to combine it all into one figure you run the risk of embedding in assumptions/biases that will skew your results without realising. It may be that the above is a fundamentally flawed approach for some reason to do with your particular business that I have no idea about so it’s worth really thinking about whether there are other factors not considered.

Further thoughts:

1. A month’s data probably isn’t sufficient for you to see a trend, particularly if the data’s quite noisy.

1. Are there any periodic fluctuations to consider eg there’s a staff meeting on Monday mornings that means all C/D’s are busy, or that the type of business you get on weekends vs weekdays tends to be different?

1. Obviously the most judgmental part of my suggested method above is the weightings you use in step 2. You should try flexing these to see what difference it makes to your conclusions.

I don’t have anything to add but this thread makes me so happy love data!

Hello to the statisticians out there!

Some nice suggestions here. I’d be tempted to run a cluster analysis on this data as an exploratory step. Also to make job level a multinomial variable for regression and set the lowest grade as the reference category.

What we need is for OP to share her data, then you statisticians to each build a predictive model (I'm an actuary, so I just play at being a statistician ), then we test them on a fresh month's dataset...

How is performance calculated? Currently you only have a theory that it is down to mix of staff bands but there could be huge numbers of other factors.

I think you'd need some hypotheses of which staff mixes work best which you could then test

I'm now tempted to sign up for an OU Stats based course as I love data and messing about at a very very basic level - but can only dream of the analysis that you are at!! This is like reading soft porn!!

Have you asked the staff which people they feel they work well with?

So many factors to look at - day of the week, weather, holiday periods.....

Do you have different leaders? Who plays what role?

Waking up to this has made me so happy!

Yes the data is from the NHS. I didnt' want to say because honestly i'm planning on passing this work off as my own (I jest)

I have at least 3 months data at the moment. Performance is measured by how many people are seen and discharged or admitted by 4 hours. Amount of clients is 'attends'. Mix of staff are grades of doctors.

I would love to share this data but I don't think I would be allowed!

Someone else was correct that interactions are absolutely a factor, 300 people with a cold and a hurty finger are obviously different to 300 people having heard attacks.

I'm looking for a rough idea really because the data doesn't do what it is supposed to do. We can have low attends and a high grade staff mix but crappy performance. Something has to be affecting it and I thought I would look at the staff mix first. It could absolutely be the type of injuries/illness but over 3 months you would think that would even itself out? It is pretty consistent over the three months!

I think initially I’d look at it quite simply. A month isn’t long enough to show trends though.
We have analysts who do full on statistical analysis but I’d want an initial simplified understanding to discuss with them whether it was a useful tool.
An ordinary excel spreadsheet with lines of staff grade total numbers.
Then a line with performance RAG rated. 90% plus green, 85 - 90% amber and below 85% red. You’d need to adjust intervals depending on range of performance.
Then another line with attendance numbers.

At a glance you can see where red days are and look at staffing model on those days ( so 80% of red days had a lower skilled team, for example). Over time you should produce evidence to show that on days with a lower skilled team the throughput was less and performance was lower (or not).

It’s quite simple data and doesn’t need to be over complicated. It doesn’t however consider other influential factors.

There is a very good A and E dashboard available to measure exactly this.

In my opinion, I think you'd have to grade the attendees as well, so how many high, how many medium and how many low 'need' interactions so that you can map it across.

I'd also then look at the top and bottom 10% performance rather than try to find an ideal mix; as that doesn't really happen in real life. I'd find out what was going on to make the top 10% performance happen, and what was going badly to make the lowest 10% performance happen; and look at outlying factors that may have influenced this before trying to make assumptions on performance by staff mix at this stage.