Lecture 4 - Probability, Sampling and Distributions

Question 1

Define probability theory

Answer 1

The branch of mathematics concerned with the study of random phenomena, i.e. chance.

Question 2

Using the Gaussian equation, we can predict the value of y for any value of x from just the…

Answer 2

Mean and standard deviation

Question 3

A positive skew moves the data peak of a normal distribution to the…

Answer 3

Left, and vice versa for a negative skew

Question 4

Pearson’s coefficient of skew uses… to…

Answer 4

The difference between the mean and median… Measure the skew in terms of both magnitude and direction (positive or negative)

Question 5

When data is positively skewed, i.e. the tail is on the right of the mean, mean>…

Answer 5

Median>mode

Question 6

When data is negatively skewed i.e. tail is on the left of the mean, mean<…

Answer 6

Median<mode

Question 7

What percentage of the sample are within 1 s.d. of the mean?

Answer 7

68%

Question 8

What percentage of the sample is within 2 s.d.s of the mean?

Answer 8

About 95%

Question 9

What percentage of the sample is within 3 s.d.s of the mean?

Answer 9

About 99.7%

Question 10

Parametric tests assume that the mean and standard deviation…

Answer 10

Accurately represent the population distribution

Question 11

Data can be transformed by…

Answer 11

Performing a mathematical operation (s) on all the values recorded

Question 12

Data transformation is useful for…

Answer 12

+ reducing the impact of outliers/skew
+ standardisation, e.g. z scores are a consistent, universal unit
+ to remove non-linear effects
+ theoretical - using different measures to better understand the data
+ making the data normally distributed so that parametric tests can be used.

Question 13

The z score is calculated by…

Answer 13

Taking the mean from each score and dividing the result by the standard deviation

Question 14

The z score tells us…

Answer 14

How many standard deviations we are above or below the mean (0)

Question 15

Sampling error is the difference…

Answer 15

Between the mean of each sample and the true mean of the population (and other sample means)

Question 16

The standard error of a statistic tells us…

Answer 16

How much how much that statistic is likely to vary from one sample to another

Question 17

The standard error of the mean is…

Answer 17

A measure of how confident we are that we know the true population mean, calculated by dividing the standard deviation by the square root of the sample size.

Question 18

S.e.m. is dependent on…

Answer 18

• The standard deviation of the population (variability of the original data) - smaller = more representative, higher confidence level
• The number of data used to create the sample mean - larger sample size = more representative, higher confidence level

Question 19

Confidence intervals are often used as an alternative to…

Answer 19

S.e.m.

Question 20

A confidence interval of a certain percentage indicates…

Answer 20

The likelihood of that range containing the true mean

Question 21

Confidence intervals are computed by…

Answer 21

Multiplying the s.e.m. by the s.d. values you want it to be between, e.g. for a 95% c.i. multiply by +-1.96

Question 22

Error bars can be…

Answer 22

Either 95% c.i.s or s.e.m.s.

Question 23

The normal distribution, using various methods, allows us to determine:

Answer 23

• the probability of a certain score or range of scores occurring
• the probability that the population mean falls within a certain range
• the probability that populations are different, e.g. through error bar differences