PART II: Python For Basic Data Analysis

Question 1

What are the functions you have to import to plot/show a graph?

Answer 1

From pylab (or matplotlib) and numpy
Plot, show, xlabel, title, legend, xlim, etc
-import data using loadtxt
-use linspace to get x values and then calc y
-assign x and y manually with lists
-can also use errorbar()

Question 2

How can we modify the lines and colours on a plot?

Answer 2

Colours: r,g,b,c,m,y,k,w

Line styles: o(dotted), -(solid), –(dashed)

Question 3

Scatter plots

Answer 3

Use scatter() from pylab
For if you don't want to connect the dots

Question 4

Density plots

Answer 4

• for chi^2 mostly
• use imshow() from pylab
• y axis top to bottom, x left to right
• adjust y with origin=”lower”
• parameter extent=[xl,xu,yl,yu] gives range of x and y values
• aspect=# specifies aspect ratio of x and y axes
• colorbar() shows range of colours to help read density plot
• also different colour schemes exist! (Ex. spectral() )

Question 5

What kinds of errors or uncertainties are there?

Answer 5

Systematic: error only goes one way
Random: goes both ways at random

Question 6

What is discrepancy?

Answer 6

Refers to the difference between results

Question 7

When is discrepancy significant?

Answer 7

If it’s larger than both error ranges combined (as in, there’s no overlap of error bars)

Question 8

When are the two measurements not consistent?

Answer 8

If the discrepancy is significant

Which means if it’s larger than both error ranges combined

Question 9

Error propagation: sums, differences, products, quotients, how???

Answer 9

Sums and differences add in quadrature (sum of squares)
Products and quotients add RELATIVE error in quadrature
Follow BEDMAS

Question 10

Error propagation: two correlated or dependent conditions

Answer 10

Condition with lowest error is considered in error calculations

Question 11

What is probability?

Answer 11

The chances of getting a subset N outcomes from a total T possible outcomes:
P = N/T

Question 12

Properties of probability?

Answer 12

• 0<p></p>

Question 13

What do we do if we have two independent conditions? (Probability)

Answer 13

Neither can affect the probability of the other and so probabilities are multiplied

Question 14

How do we represent statistical significance?

Answer 14

• we use n*sig (corresponds to probability of having a result n standard deviations away from mean in Gaussian dist)
• 1sig = 0.31
• 2sig = 0.0456
• outcomes are significant if p-value is equal to sig level
• assume two sides probabilities

Question 15

Define p-value

Answer 15

Probability that our data matches the null hypothesis
Higher = greater match to “nothing happening”
Lower = more different and significant results compared to control/null hypothesis

Question 16

How do we calculate mean/average?

Answer 16

List: sum/len
Array: sum/shape (from numpy)

Question 17

What is the median?

Answer 17

For sorted set of values: numpy.median()

Question 18

Mode

Answer 18

Most common value of x

Have to count occurance of each quantity

Question 19

Formula for variance

Answer 19

Sig^2 = 1/N * sum(N,i)(xi-xavg)^2

Question 20

What is variance?

Answer 20

If we’re looking at the range/spread of values, it means how far from the average we usually are

Question 21

Error in the mean: what is it, what’s the formula?

Answer 21

Measure of how reliable your mean value is
Delta = sig/sqrt(N)
You want more N to reduce it
You’d have to increase N a lot though since its sqrt

Question 22

Formula for normal/Gaussian distribution

Answer 22

p(x) = 1/sig*sqrt(2pi) * exp(-(x-xavg)^2/2sig^2)

Question 23

Central limit theorem

Answer 23

Distribution of sample means approaches a normal distribution as sample size gets larger

Question 24

How do we calculate the probability of a given result for a normal distribution?

Answer 24

Integrate it
But you can’t integrate it so
We have erfc and erf
P(|x|>nsig) = erfc(n/sqrt(2))

Question 25

When do you use binomial distribution?

Answer 25

When you want to determine the probability of discrete events occurring, with no range given

Question 26

Binomial distribution: what do the variables mean?

Answer 26

K is number of discrete events you’re looking for
N is total number of events
P is probability of discrete event occurring

Question 27

When do you use poisson?

Answer 27

Probability of discrete events occurring

Rate is given (as lambda)

Question 28

When you’re picking out errors in code, what should you look for?

Answer 28

Float values

Syntax errors

Question 29

What are the largest/smallest numbers in Python for floats and what happens if you exceed them?

Answer 29

\+/- 10^308
Exceeds max: inf (overflow)
Lower min: 0 (underflow)
Operations with inf give nan
Limited precision due to rounding error

Question 30

Precision for int values in Python?

Answer 30

Arbitrary precision (as long as needed)

Question 31

What is maximum likelihood?

Answer 31

A way of finding the most probably model used to reproduce the data you obtained
Method of fitting a curve

Question 32

How good is a model?

Answer 32

Log values of probability to force it to be monotonic

To max it you use chi^2

Question 33

How do we test our models?

Answer 33

Guess better parameter values

Use least-squares test to find lowest values of chi^2 (mathematically or density plot)

Question 34

How do we run the chi^2 process?

Answer 34

Import functions and data
Set different ranges of a,b using set intervals to test
Create array to store all chi^2 values for a,b
Create for loop to calc/store all chi^2
Use density plot or solve mathematically to find lowest chi^2

Question 35

Solving chi^2 with math

Answer 35

Use chi^2 equation & plug in model for m
Differentiate chi^2 with respect to a, set =0
Solve for a
That looks simple but it’s ugly

Question 36

What do you do if it isn’t a linear model?

Answer 36

Use a density plot