I have scatterplot in Tableau, and I displayed trendlines. However, I cannot understand why there are three of them.
When I research this on Tableau, they say upper line is upper 95% confidence, and lower line is lower 95% confidence.
When I think of confidence levels, I think if there are 100 black and white marbles and I take a sample, and see the ratio, I can say 95% of the time, white marbles will be 40% to 60%
And to create confidence bounds, 92% to 98% of the time, white marbles will be 40% to 60%
But I'm having difficulty translating this to tableau trendlines. Please advise.
Think of your data set as just one random sample drawn from a larger population of possible data sets. You could have sampled another time or place or in a parallel universe.
If you could build a scatter plot for the entire population, it would have a best fit trend line also. You can think of your trend line as a sample trend line attempting to estimate this true population trend line.
Now imagine you actually did collect many different sample data sets from that same population. Also imagine you used identical procedures to create scatter plots and trend lines for hundreds or thousands of these data sets (samples). Different samples would lead to (slightly?) different trend lines in each plot.
The confidence bands are constructed in such a way that you can expect them to enclose the true population trend line in 95% of your samples.
You are using statistical inference to estimate the confidence in the population trend model parameters. All based on the Central Limit Theorem.
Related
When to use min max scaling that is normalisation and when to use standardisation that is using z score for data pre-processing ?
I know that normalisation brings down the range of feature to 0 to 1, and z score bring downs to -3 to 3, but am unsure when to use one of the two technique for detecting the outliers in data?
Let us briefly agree on the terms:
The z-score tells us how many standard deviations a given element of a sample is away from the mean.
The min-max scaling is the method of rescaling a range of measurements the interval [0, 1].
By those definitions, z-score usually spans an interval much larger than [-3,3] if your data follows a long-tailed distribution. On the other hand, a plain normalization does indeed limit the range of the possible outcomes, but will not help you help you to find outliers, since it just bounds the data.
What you need for outlier dedetction are thresholds above or below which you consider a data point to be an outlier. Many programming languages offer Violin plots or Box plots which nicely show your data distribution. The methods behind plots implement a common choice of thresholds:
Box and whisker [of the box plot] plots quartiles, and the band inside the box is always the second quartile (the median). But the ends of the whiskers can represent several possible alternative values, among them:
the minimum and maximum of all of the data [...]
one standard deviation above and below the mean of the data
the 9th percentile and the 91st percentile
the 2nd percentile and the 98th percentile.
All data points outside the whiskers of the box plots are plotted as points and considered outliers.
This query refers to decomposition of classic Airline passengers data into Trend, Seasonal and Residual. We expect linear trend to be a straight line. However, the result is not so. I wonder what is the logic behind extraction of Trend. Can you please throw some light?
from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(airline['Thousands of Passengers'], model='additive')
result.plot();
Two things to clarify:
1) Not all trends are linear
2) Even linear trends can be subject to some variation depending on the time series in question.
For instance, let's consider the trend for maximum air temperature in Dublin, Ireland over a number of years (modelled using statsmodels):
In this example, you can see that the trend both ascends and descends - given that air temperature is subject to changing seasons we would expect this.
In terms of the airline dataset, we can see that the trend is being observed over a number of years. Even when the observed, seasonal and residual components have been extracted, the trend itself will be subject to shifts over time.
I created a plot in Tableau with a line of best fit using the "Trend Line" feature under "Analytics". This plots a line of best fit, with optional confidence bands around that line.
Here's a screenshot of my plot
My question is: how do I edit how wide or narrow the confidence bands around the line of best fit are? I read somewhere that they default to 90% or 95% confidence. I want to be able to widen or narrow those lines by increasing or decreasing the confidence. My goal is to make the bands more narrow.
I couldn't find how to do this online after a lot of searching. Any help is much appreciated!
Thank you
The confidence band for trend-lines cannot be altered in the same way they can be for other trending analytics (such as forecasting). In fact, within Tableau trend-line confidence bands cannot be altered at all.
In order to make the bands more narrow you would need to find a better fitting trend-line. To do this you can right click on the trend-line and click edit and play around with logarithmic, exponential & polynomial options.
I believe that the trendline confidence bands in Tableau cannot be altered because it represents the potential error as calculated from the StdError. This is the deviation around the trend-line from actual data points and is unrelated to confidence %s.
You can see this by right clicking on the trend line in Tableau and clicking 'Describe Trend Line'. This will open a dialogue which describes the derivation of the trend-line. What you will find is the Confidence interval will be drawn the width of the StdError.
I have constructed a GMM-UBM model for the speaker recognition purpose. The output of models adapted for each speaker some scores calculated by log likelihood ratio. Now I want to convert these likelihood scores to equivalent number between 0 and 100. Can anybody guide me please?
There is no straightforward formula. You can do simple things like
prob = exp(logratio_score)
but those might not reflect the true distribution of your data. The computed probability percentage of your samples will not be uniformly distributed.
Ideally you need to take a large dataset and collect statistics on what acceptance/rejection rate do you have for what score. Then once you build a histogram you can normalize the score difference by that spectrogram to make sure that 30% of your subjects are accepted if you see the certain score difference. That normalization will allow you to create uniformly distributed probability percentages. See for example How to calculate the confidence intervals for likelihood ratios from a 2x2 table in the presence of cells with zeroes
This problem is rarely solved in speaker identification systems because confidence intervals is not what you want actually want to display. You need a simple accept/reject decision and for that you need to know the amount of false rejects and accept rate. So it is enough to find just a threshold, not build the whole distribution.
I have several curves that contain many data points. The x-axis is time and let's say I have n curves with data points corresponding to times on the x-axis.
Is there a way to get an "average" of the n curves, despite the fact that the data points are located at different x-points?
I was thinking maybe something like using a histogram to bin the values, but I am not sure which code to start with that could accomplish something like this.
Can Excel or MATLAB do this?
I would also like to plot the standard deviation of the averaged curve.
One concern is: The distribution amongst the x-values is not uniform. There are many more values closer to t=0, but at t=5 (for example), the frequency of data points is much less.
Another concern. What happens if two values fall within 1 bin? I assume I would need the average of these values before calculating the averaged curve.
I hope this conveys what I would like to do.
Any ideas on what code I could use (MATLAB, EXCEL etc) to accomplish my goal?
Since your series' are not uniformly distributed, interpolating prior to computing the mean is one way to avoid biasing towards times where you have more frequent samples. Note that by definition, interpolation will likely reduce the range of your values, i.e. the interpolated points aren't likely to fall exactly at the times of your measured points. This has a greater effect on the extreme statistics (e.g. 5th and 95th percentiles) rather than the mean. If you plan on going this route, you'll need the interp1 and mean functions
An alternative is to do a weighted mean. This way you avoid truncating the range of your measured values. Assuming x is a vector of measured values and t is a vector of measurement times in seconds from some reference time then you can compute the weighted mean by:
timeStep = diff(t);
weightedMean = timeStep .* x(1:end-1) / sum(timeStep);
As mentioned in the comments above, a sample of your data would help a lot in suggesting the appropriate method for calculating the "average".