# Experimental design and analysis

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- Created by: amy.louise
- Created on: 14-01-16 20:46

What is probability?

How likely an event will happen

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How is probability expressed?

A number (P-value)

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What is the maximum and minimum value probability can be?

0 and 1

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What does the sum of probabilities for all outcomes equal to?

1

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How can you calculate probability?

number of times an event happens / number of repeats

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What does the null hypothesis state?

That there is no relationship between two measurements

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What does a small p-value suggest?

That there is strong evidence that the null hypothesis is wrong

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What does a large p-value suggest?

That there is strong evidence that the null hypothesis is correct

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What would a p-value above 0.05 suggest about the difference?

Its due to chance

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When are two events mutually exclusive?

When they can't occur at the same time

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What is conditional probability?

The probability of event A occurring if event B has occured

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What is the rule of subtraction?

Finding the probability of event A occurring by doing 1-(P A not occuring)

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What is the rule of multiplication?

Finding the probability of both events A and B occurring. (pA x pB if A has occured)

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What does statistical interference mean?

Drawing conclusions about an observation based on data

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What is random sampling?

Sampling when the probability of including an individual from a population is the same for all individuals and is independent of other samples

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What is bias sampling?

Sampling when the probability of an individual being picked to be sampled from a population is increased or decreased due to its characteristics

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What is non-independant sampling?

Sampling when the probability of an individual being picked from a population to be sampled is dependant on other individuals from the population

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What is a type I error?

When you reject a null hypothesis which is actually correct. You think theres statistical difference when there isn't

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When are type I errors most commonly made?

When there is multiple testing

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When would you use a bonferoni correction?

In order to reduce type I errors. When an experiment is testing many hypotheses

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What does the bonferoni correction do?

Tests hypotheses to a certain statistical significance. 0.05 / no. of hypotheses

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How does the bonferroni correction work?

Because the probability of getting at least one significant result increases as the number of hypotheses increases

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What is a type I error also known as?

A false negative

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What is a type II error?

When you accept the null hypothesis but its actually false. When you think theres no significant difference but there is

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How can you reduce the chance of making a type II error?

Ensuring your test has enough statistical power

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What is statistical error?

The likelihood that a study will detect an effect if there is a true difference to be seen

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What is statistical error mainly effected by?

Same size and size of the effect

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What is the effect size?

How big the effect of a variable had on samples

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Does binomial distribution had a certain number of repeats?

Yes

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What are the outcomes of a binomial experiment?

Success or failure

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What is Q in a binomial experiment?

The probability of failure (1-P)

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What is the binomial probability?

The probability that n-number of trials results in exactly X successes when the probability of a success is P

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Does binomial distribution had a certain number of repeats?

No it has infinite trials

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What has to be know in a poisson experiment?

The average number of successes that occurs within a specific region

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What can a 'region' be in a poisson distribution?

Time, length, volume

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What is the poisson probability?

The probability that exactly x successes will occur when there is a mean number of successes

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Wha type of data do you use a chi-squared test for?

Nominal data that falls into particular categories

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What does a one-factor chi-squared test do?

Compares expected values against observations of one variable

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What does a two-factor chi-squared test do?

It tests two variables and identifies whether the factors are independent of each other

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What is the null hypothesis in this test?

That there is no relationship

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What is continuous data?

Data that has a unit and can be measured

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What does the curve of normally distributed data depend on?

The mean and standard deviation from the mean

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What doe the mean determine on the graph?

The location of the centre of the graph

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What does the standard deviation determine?

The width and height of the graph

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What is the total area under the graph equal to?

1

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What % falls under 1 standard deviation of the mean?

68%

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What % falls under 2 standard deviation of the mean?

95%

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What % falls under 3 standard deviation of the mean?

99.7%

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What does the Shapiro-wilk test for?

Normality of data

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What does it allow you to see?

The distribution of your data

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hIf the P-value is below 0.05 is the null hypothesis accepted/ rejected?

rejected

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Is data normally distributed with a P-value of more than 0.05

Yes

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What is the t-test used for?

To estimate the population parameters when the sample size is small or the population variance is unknown

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What are parameters?

Numbers that summers data of a population. The mean and the standard deviation from the mean

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Can a population distribution be directly calculated?

No, only estimated

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What does the central limit theorem state?

That the sample mean of a statistic will follow a normal distribution as long as the sample size is large

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If your sample size is small or you don't know the standard deviation of your population, what can you do?

Look at the distribution of the t-statistic

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What does the standard error of the mean tell you?

It tells you how different the sample means are from the population mean

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What is a confident interval?

A range of estimated values that will likely contain the population mean

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What are confident limits?

The upper and lower boundaries of the confident interval

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Is the standard deviation of large samples always the same?

Yes at 1.96. over 30 samples

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What if you have a small sample size?

The standard deviations need to be adjusted

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Is the standard deviation of a small sample size bigger or smaller than that of a big sample size?

Bigger

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What is a t-value?

The difference between the standard deviation of the population and the sample.

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What is a confidence level?

A percentage that tells you how many of the samples you can expect to include the true population mean within their confident intervals

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What does a wide confidence interval suggest?

That you need a bigger sample size?

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Is it good to have a narrow confidence interval and why?

Yes because it is more precise

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How do you calculate variance?

Squared standard deviation

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How do you calculate the confidence interval?

The sample mean + and - the standard error

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What does a two-sample t-test measure?

It measures if themes of the two samples differer from the population mean and from each other

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What is the test statistic of this test?

Z

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When do you use ANOVA?

When you are comparing two or more variables

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What are the assumptions of ANOVA?

The variance of all the errors are the same, The errors are independent and they are normally distributed

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What does ANOVA test?

If the value of the variables differers significantly among 3 or more values

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What do you need to calculate in ANOVA?

The grand mean and group mean

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What is the F statistic ratio?

The between group variance / The within group variance

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What effect does a higher between group variance have on F?

Increases it

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What effect does a large amount of variance, due to chance, have on F?

Decreases it

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What does a high F value suggest?

Moe significance and difference is not due to chance

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How do you calculate sum of squares?

Data point - mean ^2

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When do you use a Mann whitney U test?

When you're data is not normal and you are testing one variable

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What parametric test is the Mann whitney U test compared to?

T-test

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How do you display data for a Mann whitney U test?

Rank it in ascending order

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Whats the next step?

You compare the two data points in each rank and find the difference. Ua and Ub

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Are the differences separated between when the X column is bigger and then when the Y column is bigger?

Yes

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What is the U value?

The ratio of Ua to Ub

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when do you use a Kruskall wallis test?

When the assumption of ANOVA are not met. Data is not normally distributed and there are not equal variances

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What is the null hypothesis?

The sample are from the same population

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Does Kruskall wallis involve ranking data too?

Yes

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What is the test statistic?

H

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What is the kruskall wallis test used for?

When two factors are being tested

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What is the limitation of the kruskall wallis test?

It only tells you that there is a difference or not between two groups. It doesn't tell you which groups

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What does two-way ANOVA test?

It compares the mean difference between groups that have multiple factors

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What types of variables must two-way ANOVA include?

Two nominal variables and one measurement variable

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Wat do you test?

What effect each nominal variable has on the measurement variable

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When would you transform data?

When it is not normally distributed

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How do you transform data?

Apply a log transformation. Base 10 (log10)

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Are you able to do statistical tests on transformed data?

Yes

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What does a correlation (r) measure?

The extent to which two variables change together

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What is the measurement of a correlation?

The correlation coefficient r

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What does r range from?

-1 to +1

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What would -1 and +1 tell you about the line?

Its a completely straight line where all points are on the line

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What doe a correlation look for?

A linear effect

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What unit does r have?

No units

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How do you calculate a correlation?

Calculate the sum of squares for the Y and X values then calculate the sum of cross products by adding them together

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What is r^2?

A coefficient of determination

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How many samples does a test need t give a significant r?

3

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What is regression?

It calculates the 'best' straight line through the plots in order to express the relationship of the correlation coefficient

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What is the regression line?

A line that minimises the sum of squared deviation of the plots from the line

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What is the intercept symbolised as?

c

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What is the intercept?

The point at which the line crosses the x-axis

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What is the slope symbolised as?

B

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What is the slope?

The gradient of the line

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How do you calculate the intercept?

The mean of Y - (mean X x b)

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What statistical test do you use to test the significance of regression?

Pearsons correlation

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Can you use not normally distributed data in regression?

No you must first transform the data

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What do yu do if the data does show relationship but its not linear?

Use a spearmint rank correlation test

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What type of data is linear models used on?

Normal data

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What type of data is generalised linear models used on?

Non-normal data/ count data

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## Other cards in this set

### Card 2

#### Front

How is probability expressed?

#### Back

A number (P-value)

### Card 3

#### Front

What is the maximum and minimum value probability can be?

#### Back

### Card 4

#### Front

What does the sum of probabilities for all outcomes equal to?

#### Back

### Card 5

#### Front

How can you calculate probability?

#### Back

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