Review of Fundamentals

Question 1

Why do we need statistics?

Answer 1

Reasonable people eyeballing would likely disagree if treatment was effective or not

Question 2

What is the use of statistics?

Answer 2

Help us determine if the relation between two variables is large enough so that we can assume it did not happen by chance

Question 3

What are the four steps of null hypothesis testing?

Answer 3

1st – assume that in the population groups are not different
2nd – calculate the statistic of interest
3rd – ask: if groups are not different than population, what is the probability of getting a difference this large by chance?
4th – Determine whether or not to reject H0

Question 4

What Does it mean that something is Statistically significant?

Answer 4

It would be very unusual to get this difference if chance variation were the only thing. Only 5 (p < 0.05), or 1 (p < 0.01), times out of 100. Therefore, there must be something other than chance.

Question 5

Define variance

Answer 5

Average, squared, variation in a set of scores

Question 6

What is the formula for variance?

Answer 6

V = ∑(X - M)^2 /(N - 1)

Question 7

What is the standard deviation (SD)?

Answer 7

The square root of the variance

Question 8

What is the advantage of using standard deviation instead of variance?

Answer 8

Variance is in units squared, and may be confusing. Standard deviation is in the original units of the measurement.

Question 9

What are Z scores?

Answer 9

Scores transformed into units of Standard deviations (SD)

Question 10

How are Z scores related to other standard scores?

Answer 10

Z scores are the “parent” of all other standard scores, and you can easily convert from Z scores to any of the other types)

Question 11

Define skew.

Answer 11

distribution has an extended tail in one direction

Question 12

Define kurtosis.

Answer 12

flatness or peakedness of the distribution

Question 13

What % of a normal distribution is between -1SD and +1SD?

Answer 13

68%

Question 14

What % of a normal distribution is between -2SD and +2SD?

Answer 14

96%

Question 15

What is the relationship between the Frequency distribution of sample means and the distribution of original scores?

Answer 15

• Frequency distribution is narrower (means are more stable)

- SD smaller

Question 16

What is the Standard Error(SE) of the mean?

Answer 16

SD of the Frequency distribution of sample means

Question 17

What does the SE of sample means reflect?

Answer 17

the error likely inherent in any estimate of the mean (can estimate from a single sample)

Question 18

What is the relationship between N and SE?

Answer 18

as N increases, SE decreases

Question 19

What useful info does the Frequency distribution of sample means and its SD (SE) provide?

Answer 19

amount of variabilty (error) in a distribution of means

• a narrow curve with small SD → most samples provide fairly accurate estimates of the real population mean
• a wide curve with large SD → many estimates error laden

Question 20

What are Confidence Intervals (CI)?

Answer 20

bands of error around a statistic

CI = M +- SE(z score of desired alpha)

Question 21

What does a 95% CI imply?

Answer 21

There is a 95% chance that the true population statistic (mean, etc) is between upper and lower bounds.

Question 22

What is a t test?

Answer 22

a general statistical formula in which a statistic is divided by its SE.
t = statistic/SE

Question 23

How to determine statistical significance using a t test?

Answer 23

look up the probability of obtaining a given t value (with a certain sample size), if p is small (<5%) → statistically significant

Question 24

Define degrees of freedom (df).

Answer 24

• degree to which a given parameter is free to vary
• how much “wiggle room” you have in your data
• number of independent pieces of info in data

Question 25

Define Pearson correlation coefficient (r)

Answer 25

describes the degree to which 2 variables are related

• 1.0 = perfect Inverse relation
  0. 0 = no relation
  1. 0 = perfect Direct relation

Question 26

Effect Size

Answer 26

If statistically significant is the effect large or small;
d commonly used for two-group experimental research (like a z score)
d = (Me-Mc)/SD (d = 0.2, 0.5, 0.8 → sm, med, lg)

Question 27

What do t tests and ANOVA have in common?

Answer 27

they are subsets of Multiple Regression

Question 28

When is a t test appropriate?

Answer 28

only 1 independent variable (IV), and only 2 groups

Question 29

When is ANOVA appropriate?

Answer 29

more than 2 groups or more than 1 IV (will give same results as t test for 2 groups and 1 IV)

Question 30

What is a F test

Answer 30

test for significance for ANOVA

F = t^2 = V{between groups} / V{within groups}

Question 31

What is the df for an F test?

Answer 31

requires 2 df values corresponding to the treatment and error within group)
df{total} = N-1
df{treatment} = (# groups) - 1
df{error} = df{total} - df{treatment}

Question 32

What is the similarity between F in ANOVA and F in regression?

Answer 32

both divide the variance explained by the IV BY the variance left unexplained

Question 33

What is eta squared (η^2)?

Answer 33

measure of effect size (sililar to R^2)
η^2 = 0.01 small effect
η^2 = 0.1 medium effect
η^2 = 0.25 large effect

Question 34

What is Cohen’s ƒ (ƒ^2)?

Answer 34

measure of effect size (calculated from η^2)
ƒ^2 = η^2 / (1-η^2)
     ƒ^2 = 0.02 small effect
     ƒ^2 = 0.15 medium effect
     ƒ^2 = 0.35 large effect