Lecture 4 - Distributions, Introduction to Experimental Design & Statistics Flashcards
assumption of distribution in the mean:
normal
assumption of distribution in the median:
none
shape of normal distribution curve:
bell-shaped, asymptotic at the extremes, symmetrical at the mean [no skew], mean = median = mode
area under the normal distribution curve is:
directly proportional to the relative frequency of observations and their probability: p
relationship between the mean and standard deviation in normal distribution:
in a normal distribution, mean and standard deviation are independent of each other: infinitely many possible combinations of mean and standard deviation and hence infinite number of normal distributions possible
standard normal distribution (z-distribution):
- developed to compare all normal distributions
- a normal distribution with a mean of 0 and a standard deviation of 1
- area under curve is 1
poisson distribution:
often discrete, count data [often plummeting at the bottom]
binomial distribution:
proportions, binary variables [e.g. ‘heads & tails’]
statistical hypothesis:
statement about the world that can be falsified
null hypothesis (H0):
no difference, no relationship, no effect, no signal
alternative hypothesis (H1):
[normally our research hypothesis] - signal
Y variable & X variable:
Y - response (subject to hypothesis): binary, proportion, continuous, discrete
X - explanatory (object of hypothesis): binary, proportion, continuous, discrete, categorical
what axis/variable is subject of hypothesis?
the Y variable
basis of experimental design:
manipulation of the explanatory X variable
measure change in the response Y variable
can test for causation
how can we increase the power of an experiment?
through decreasing the noise - increasing sample size and randomising
statistical tests have:
• A test statistic (e.g. t, F, Chi²) with value
• Degrees of freedom
• P-value, p-value
degrees of freedom:
number of independent observations minus number of parameters we estimated from the data
figure legends:
given under the figure and should be informative; i.e. reader needs to understand the figure without reading the main text. All abbreviations etc. need to be explained.Table captions are given before the table
mean and SD of standard normal distribution (z-distribution):
standard normal distribution (z-distribution) has a mean of 0 and a standard deviation of 1
we can compare all normal distributions to the standard normal distribution by:
• converting our y into a number of standard deviations from the mean and finding the probability with which this value lies in a range
research processes include:
formulation of hypotheses, planning of experiment,
summarising & analysing data (descriptive & inferential statistics), interpretation of results
large part of the research process involves:
hypothesis testing
Statistical (null) hypothesis:
statement about the world that can be falsified; no signal
Alternative hypothesis:
signal (often our research hypothesis)
what experiments can and can’t test causation?
Correlative, descriptive studies cannot test causation; experiments that manipulate the explanatory variable can test causation
statistical tests provide:
a test statistic with value, degrees of freedom and a p-value
p-value:
probability of getting a test statistic as large as yours (or higher) if the null hypothesis is true; probability that a null hypothesis (H0) is true
how do you calculate the degrees of freedom?
number of independent observations - number of parameters we estimated from the data
figure legends are given under the inure and should be informative:
reader needs to understand the figure without reading the main text
all abbreviations etc. need to be explained, table captions are given before the table
results and methods are written in past tense, give direction of effect, test statistics are given in brackets
