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Statistics: > Hypothesis Testing: > Flashcards

Hypothesis Testing: Flashcards

1
Q

What are some limitations of hypothesis testing?

A
  • Difficult to understand what a hypothesis test is telling you
  • Cannot make scientific decisions based on hypothesis testing alone
  • Have to consider how plausible the result is
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2
Q

Is 59 heads from 100 throws evidence of an unfair coin or Random variation?

A

Usually you would expect only getting 50 heads, but I don’t believe 59 heads is far enough from this statistic in order to be significant enough to suggest the coin is unbiased (therefore, I believe it is due to random variation)

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3
Q

What is the threshold used to determine whether the chances of something happening are due to chance or not? How is it determined?

A

This threshold is called the significance level

It depends on the experiment

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4
Q

What is the usual significance level?

A

5%

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5
Q

What is used to denote the proportion of false positives if the null hypothesis is true (the significance level)

A

α (alpha)

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6
Q

How do you calculate the critical value?

A

The critical value is the number marking the point where, above or below which, is one or both extreme(s) of the distributions. This usually covers a certain percentage (5% coverage = 0.05 significance level)

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7
Q

List the names of the two hypothesis:

A
  • H0 (null hypothesis)

- HA (alternative hypothesis)

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8
Q

What is the null hypothesis?

A

There is no significance difference- no effect (the initial assumption that we make)

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9
Q

What is an Alternative hypothesis?

A

Suggests there is a significance in the results and is an alternative theory to the null hypothesis

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10
Q

What is the relationship between the null hypothesis and the alternative hypothesis?

A

They are mutually exclusive (can’t happen at the same time)

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11
Q

How does hypothesis testing work to prove a hypothesis?

A

It assumes that the null hypothesis is true until there is significance proof that the null hypothesis is false (this doesn’t prove that the alternative hypothesis is correct)

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12
Q

What is the name given to the percentage area of a distribution marked by the critical value?

A

The critical region

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13
Q

What happens if a value given falls within the critical region?

A

We reject the null hypothesis and accept the alternative hypothesis as there is a less than 5% chance of the results happening by chance, suggesting that the result is statistically significant

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14
Q

How does the alternative hypothesis vary in a two tailed test?

A

The alternative hypothesis is just any result other than the null hypothesis (one or the other extreme)

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15
Q

What happens to the significance level during a two tailed test?

A

It is split into half of the original significance level as the critical region has to be split between both tails of the distribution while covering the same area

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16
Q

What does it mean when a result doesn’t fall within the critical region?

A

The hypothesis test does not suggest the null hypothesis is false- there is no statistical significance

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17
Q

What is the use of the critical value?

A

To determine whether the probability of getting the observed result is significant or not

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18
Q

What function is used to carry out binomial tests in R?

A

Binomial.test ( x , n , p )

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19
Q

What do x, n and p parameters in the binom.test ( x , n , p ) function stand for?

A
  • x is the observed number of successes
  • n is number of trials
  • hypothesised probability of success from null hypothesis
20
Q

What results are given when the binom.test ( x , n , p ) is used?

A
  • A title
  • A summary of data input
  • Description or alternative hypothesis
  • States p value (this is to be compared to significance level)
21
Q

What is a p value?

A

The probability of getting a result that extreme or more, assuming the null hypothesis is true

22
Q

What is an assumption made when using the p value?

A

The p value assumes that the null hypothesis is true

23
Q

What is a type 1 error?

A

A false positive

24
Q

What is it called if the null hypothesis is true and our results are not statistically significant (so we don’t reject the null hypothesis)?

A

A true negative

25
Q

When can you get a false positive (type 1 error) in hypothesis testing?

A

When your results cause you to reject the null hypothesis but the null hypothesis is actually correct

26
Q

What is a true positive in hypothesis testing?

A

When we reject the null hypothesis due to statistical significance and the null hypothesis is actually incorrect

27
Q

What is a type two error?

A

A false negative

28
Q

When do type two errors (false negatives) occur in hypothesis testing?

A

When the null hypothesis is not true but is not rejected

29
Q

What is the definition of the power of a hypothesis test?

A

The probability of correctly rejecting the null hypothesis

30
Q

What number is denoted by the letter β?

A

The area of a distribution where the null hypothesis would be rejected incorrectly

31
Q

What is the equation for power?

A

Power = 1 - β

32
Q

What is β the probability of??????

A

Getting false negatives- the overlapping area between two distributions

33
Q

How do you work out the probability of getting a false negative, true positive, true negative and false positive from a distribution?

A

. . .

34
Q

What can increase how powerful a statistical test of two overlapping distributions is?

A
  • The peaks of two distributions are well separated/ far apart
  • Large spread of values between the two distributions (how separate they are)
35
Q

How does a large spread of values across the horizontal axis make the hypothesis test more powerful?

A

There is little overlap between the distributions of both the null hypothesis and alternative hypothesis (each represented by a distribution) which has to be taken away from 1 to work out the hypothesis testing power

36
Q

What is a high false positive rate?

A

A distribution where we are more likely to accept the null hypothesis even though it is wrong

37
Q

What is effect size?

A

The combination effect of the difference between the peaks and spread of two distribution curves

38
Q

What effect does a larger effect size have on detecting the difference between distributions with similar peaks/ more overlaps but where the null hypothesis is wrong? Give an example

A

Making it easier to detect a difference distributions where the null hypothesis is incorrect but the results only differ from it slightly.

Eg. It is easier to detect a biased coin which lands on heads 80% of the time than that of 60% of the time in hypothesis testing

39
Q

What is an effect of a larger effect size on the power of a hypothesis test?

A

It provides a more powerful hypothesis test

40
Q

How can the spread of a distribution be increased to make the hypothesis test more powerful?

A

By increasing the number of trials, which increases the range of spread of data between the distributions as both have to cover a larger range of data in the horizontal axis (while the number of outcomes stays proportional). This means there is a smaller area of overlap

41
Q

What is a disadvantage of increasing the number of trials in order to increase the power of hypothesis testing?

A

This can be tedious, costly and time consuming

42
Q

What effect size would result in the most statistically powerful experiment?

A

Low dispersion and high difference between peaks

43
Q

What is the equation for effect size?

A

Dispersion (spread) + peak difference

44
Q

When are dispersion spread and number of trials more closely linked during hypothesis testing?

A

During binomial distribution

45
Q

What are standard significance levels?

A
  • 0.05
  • 0.01
  • 0.001

Statistics: (5 decks)

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