Data and distributions Flashcards

1
Q

Fundamental features of a dataset

A

Datapoints (n)
Measures of central tendency (mean, variance, SD)
Type of distribution

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2
Q

Key properties of the normal distribution

A

Continuous data
Bell shaped curve

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3
Q

How do we define the normal distribution?

A

By the mean and SD

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4
Q

In normally distributed data, 95% of the data lies within…

A

1.96 SDs of the mean

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5
Q

Properties of the Poisson distribution

A

Discrete data
As the mean gets bigger, the distribution becomes more like the normal distribution

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6
Q

When the mean is > ___ you can approximate the Poisson distribution with a _____ distribution

A

5
Normal

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7
Q

Poisson distributions are right-skewed for ____ means

A

Low

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8
Q

As the mean gets _____ in a Poisson distribution, it gets more like the _____ distribution

A

Bigger
Normal

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9
Q

Properties of the Binomial distribution

A

Discrete variables
Defined by the number of trials and the probability of one of two possible events happening

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10
Q

How do we define the Poisson distribution

A

By the mean
Mean = variance

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11
Q

How do we define the Binomial distribution?

A

Number of trials (n)
The probability of one of two events happening (p)

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12
Q

When p is low in the Binomial distribution, we see a _____ skewed distribution

A

Right
(Most of the time the event will not happen)

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13
Q

When p is very high in the Binomial distribution, we see a _______ skewed distribution

A

Left
(Most of the time the event will happen)

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14
Q

As p increases in the Binomial distribution, the distribution becomes more…

A

Bell shaped (like the normal distribution)

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15
Q

What sort of data is normally distributed?

A

Means of samples of random variables
Quantities that are the sum of many independent processes
Body temp
Brain size

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16
Q

What sort of data is Poisson distributed?

A

Counts of independently occurring events in homogenous units
E.g. Quadrat sampling

17
Q

What sort of data is Binomially distributed?

A

Counts (or proportions) of ‘successes’ vs ‘failures’ out of a fixed number of trials, where the probability of success is constant
Number of ‘heads’ in 10 coin flips
Proportion of a population with a particular mutation
Number of adult frogs developing from fixed initial number of tadpoles

18
Q

What is the 95% confidence interval for a mean?

A

An interval of numbers that will contain the true value of the mean 95% of the time

19
Q

How to calculate standard error of the mean

A

standard deviation / root(n)

n = sample size

20
Q

As the sample size increases, standard error gets _____

A

Smaller
As n increases, so does root n, so the standard deviation is being divided by a larger number and therefore gets smaller

21
Q

The smaller the sample size, the _____ the confidence interval needs to be to ensure an x% chance of containing the true value of the mean

22
Q

When we don’t know the standard deviation of the population precisely, we have to use ______ to calculate the confidence interval

A

A t-distribution

23
Q

How to calculate a confidence interval

A

CI = mean +/- tcrit x SE

24
Q

Approximate rule of thumb for 95% CI

A

mean +/- 2 x SE of the mean

25
The 95% confidence interval is _____ than the 99% confidence interval
Narrower
26
What is the null hypothesis?
There is no significant difference between the populations we are looking at
27
What is the alternative hypothesis?
The hypothesis that something will happen (there will be an effect of a drug, two groups will be different etc)
28
What is a two-tailed test?
A hypothesis test where we don't have any reason to suppose that the effect will be in a particular direction
29
What is a one-tailed test?
A hypothesis test where we have reason to believe that the difference will be in a specific direction