Statistics

Question 1

What is a probability distribution?

Answer 1

It is a mathematical description of the probabilities of events in a sample space which includes all possible outcomes or results of that experiment. A lot of continuous data in normal populations can be well represented by a normal distribution or we can usually make it one if it doesn’t. So if we take the entire population and measure lots and lots of basketball throws worth of accuracy there a good chance that the variation in the population will be somewhat normally distributed. So in a typical normal distribution such as this one, approximately 68% of the data/outcomes fall within one SD of the mean, within two SD is 95% of the data so only 5% fall in the two tails.

Question 2

What measures does the t-statistic take into account?

Answer 2

The t-statistic takes into account both the expected mean and a measure of the standard error of the mean based on the sample

Question 3

What is the z-distribution?

Answer 3

Standard normal distribution. Has a mean of 0 and an SD of 1

Question 5

When would you use a t-distribution over a z-ditribution?→When you don’t know the population values

Question 7

What affect does degrees of freedom have of the distribution of t-values?→Depending on our df

Answer 7

the resulting distribution of t-values varies: It looks broader for lower df and more like a normal distribution for larger df

Question 9

When do you use a one-sample experimental design?→We have one group with values coming from different people. This is compared to a single value

Question 11

What are some advantages and disadvantages of one-sample experimental design?→Advantages: Can be used to compare group data to known values. Disadvantages: We may not always know population values

Answer 11

We may want to compare two groups

Question 12

When do you use a between-groups/ independent-measure design?→We have two groups

Answer 12

and the values come from different people (i.e.

Question 14

What are some advantage and disadvantages of between-groups/ independent-measure design?→Advantages: The measurements are independent

Answer 14

We don’t have to worry about learning effects due to repeated exposure. Disadvantages: People in the different groups might be quite different in various ways: Personality

Question 15

When do we use a within-group/ repeated measures design?→There is a single group which provides data for both conditions

Answer 15

i.e.

Question 17

What are some advantages and disadvantages of within group/repeated measures design?→Advantages: We don’t have to think about differences in baseline factors such as personality etc. because this will always affect both conditions equally. We can study changes in behaviour over time. We can usually test fewer people. Disadvantages: Measurements are not independent è we need to calculate the variance differently People know the treatment after the first condition and can’t be naïve in the second round. This might not work for every experiment. We need to carefully counterbalance the conditions to avoid unwanted order effects

Question 19

What type of t-test do we use for a non-direction hypothesis?→A two tailed t-test

Question 21

When do we reject the null hypothesis in a single sample t-test?→When the empirical t value is greater then the critical t value

Question 23

What is the equation for a single sample test value?→T equals the empirical mean from our sample take away the expected mean from the population over the standard error of the mean

Question 24

How do you calculate the estimate standard error or the mean?→Standard error of the mean equals the standard deviation over the square root of the sample size

Question 26

What is variance?→The measure of the deviation in our sample

Question 28

How do we calculate variance?→The sum of squares divided by n (sample size) minus 1

Question 31

What is the independent measures t-test equation?→https://remnote-user-data.s3.amazonaws.com/qyzLXOrRZlzO0wG3AsZd2Ut1gSljFP32ALHkdc7bxxKcGuyjAuDX1evThu36_Cio69nG7HHRCrkgXo-dM0oCC8HbIciMHb9hcSpNv-KCZZ4ufy_OWtFumEXMRtSkUjUp.png

Question 33

What is pooled variance and what is needed for it to work?→the pooled variance is the average of the two sample variances. Only works if both groups have the same sample size.

Question 35

how is pooled variance calculated?→The pooled variance is calculated by adding up the summed squared differences (SS) from each condition and dividing it by the sum of the df

Question 38

What are we testing in the paired-samples t test?→whether the average difference score is significantly different from chance

Question 40

What is the effect of sample variance on effect size?→a large sample variance s2 will make it less likely to obtain a significant effect. Inversely

Answer 40

a larger sample size n tends to produce bigger t statistics and hence more likely to produce significant results

Question 42

What are two effect size measures?→Cohen’s d

Answer 42

R squared

Question 44

What is Cohen’s d and how is it calculated?→Cohen’s d gives an estimate of the effect size that is independent of the sample size: d is the mean difference divided by the standard deviation https://remnote-user-data.s3.amazonaws.com/MA8PXtth4Ha_wCwAp8zAHPyzuOooJnVqw1qA64AkoSu0nIcU4zm2zXjJ_VsA_mU5-cyqgIDliFy4eN50F5Z9i8mpPjxHbDH6JlvJg-vEwoEn3qcljwGwqzzqVdQOKHz-.png

Question 47

What are the effect size measures for Cohen’s d?→https://remnote-user-data.s3.amazonaws.com/PcP8amCNweUYYwpDVsZkgHdWBZBWERhuJVfS7BAwtHB5LkFPNp7FNZ-awxtcNuhgjJcar4jWVcHhhLegWDNHz21QkPlYFybeaojCx11VsLHyWxcqsPLVLBH9WQo7AzIe.png

Question 50

What is r squared and how is it calculated?→a nother way to calculate an effect size (albeit not independent of the sample size) is to estimate the percentage of variation explained by the “treatment” (i.e.

Answer 50

our experimental manipulation): https://remnote-user-data.s3.amazonaws.com/1zYzJ_JVZlXm22eRk1ZdVSl2kXR1GfTEspWrdIO8GJ48hw8BTPhbNSrj3JkKXPBEB631hvVzbwvJBWvCozMveUJW4VQKbl83lr6drrbRYPMlRNrAVSZrzBZ53he3RWA0.png

Question 51

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Question 52

How do you interpret r squared effects?→https://remnote-user-data.s3.amazonaws.com/UtTbk_co1vJMvSU6QoSHuq8pXkx435Dl-11cc6xXiNrHU3FyP71zLrntohbVmBJKjPLgK8ko_l7flsLayq0SXxUbSp7mOFBkkDPbxY2BJ_UKd91R8hNMpz1-z7ko5EmP.png

Question 55

What is a confidence interval?→A confidence interval is an interval

Answer 55

or range of values

Question 57

What assumptions do you need to consider before deciding to run t-tests on data?

Question 58

A) The observations must be independent (this means people must not influence other people’s values; no systematic biases when assigning people to groups)

Question 59

B) The populations from which the samples are drawn must be normal (however

Answer 59

this assumption can be violated for larger sample sizes as t tests are quite robust)

Question 60

C) If comparing two populations (independent-measures t test)

Answer 60

the samples must have equal variances (if the variances are not homogenous

Question 62

What do you have to consider in relation to hypothesis testing?

Question 63

H0 is the null hypothesis

Answer 63

and H1 is the alternative hypothesis (usually

Question 64

You want to make it as difficult as possible for “your” H1 to succeed

Answer 64

ans therefore you start by initially assuming that the H0 is true

Question 65

You then calculate the probability of measuring a sample mean (M) greater or

Question 66

equal to what the H0 states (or less than depending on the hypothesis)

Question 67

Only if this probability is really very small (usually less than 5% likely)

Answer 67

you

Question 68

conclude that the H0 is probably not true and you therefore reject it in favour of the H1

Question 69

You can never state that a result has proven that the H1 is true – there is always the possibility of an error (e.g.

Answer 69

5%)