Statistical Analysis of Experimental Data Flashcards
define statistics
mathematical science that deals with chance variation
define a distribution
an arrangement of values of a variable showing their observed frequency of occurrence. can use this data to create a probability distribution plot.
how do you get a smooth and accurate bell curve on a distribution plot?
the more value you collect in your data, the more accurate the curve will be and making it more smooth as well.
define the mean
it is the average of a set of measurements that is located at the center of the normal distribution.
sum of all values/number of samples
define the sample mean
sum of all x values/number of measurements took for the sample
x = sample refers to a smaller unit of the population. as the number of samples increase, it becomes more accurate to the population mean.
define standard deviation
deviation amoun individual measurements from the population mean for the entire population
s = square root ((sum of the sample - sample mean)/ number of measurement - 1, degree of freedom)
define the relative standard deviation
standard deviation divided by the average and expressed as a percentage
%RSD = (standard deviation/ sample mean) x 100%
answer = mean +/- standard deviation, RSD
what are the 3 kinds of tests we can use to verify data sets?
T-test, Q-test, and Grubs-test
how to find a confidence interval?
range of values within, which there is a specific probability of finding the true mean.
interval = measured mean +/- (t-test x standard deviation)/square root of the number of observations
how to use the t-test?
you look at the given confidence level on the top, and then the degree of freedom (number of observations - 1) on the left hand side. find the value that aligns with both of those and that is your t-test value.
How to do a comparison of means?
We can also use the t-test to compare mean values.
t = lmean1 - mean2l/Spooled x square root (N1 x N2/N1 + N2)
for degree of freedown when comparing 2 variables, its N1 + N2 - 2!
if calc > table, difference is significant
how to use the Q-test?
Use the Q-test when you are trying to find out if 1 data point is an outlier. Can only be used once!
Qcalc = gap/range
if calc > table, then the value is removed from the data set
NO DEGREE OF FREEDOM FOR THIS! it is just the number of observations
how to use the Grubs-test?
this is another way to determine if the data set has any outliers
Gcalc = l outlier value - sample mean l / standard deviation
calc > table = data value is rejected]
CAN BE USED MORE THAN ONCE!
