Stats - Week 2

Question 1

Describing Distributions we look at what?

Answer 1

Measures of shape (Kurtosis and Skewness), central tendency (mean, median, and mode), “spread” or variation (range and variance & standard deviation)

Question 2

Distribution shapes!

Answer 2

Normal distribution, Positive skew (left), Negative skew (right), Leptokurtic(Positive kurtosis), Platykurtic (Negative kurtosis)

Question 3

Measures of central tendency =

Answer 3

= estimate the “center” of our data. Mode, Median, and Mean

Question 4

MODE:

Answer 4

most frequent score in a distribution. A distribution can be bimodal or multimodal.

Question 5

MEDIAN:

Answer 5

Middle score or 50th percentile
Arrange the scores in ascending order
Median = middle score if # of scores is odd
(average of middle 2 scores if # of scores is even)

Question 6

MEAN:

Answer 6

Arithmetic average of the scores in a distribution.
The symbol for the mean of a population is omega;
The symbol for the mean of a sample is. (SUM) Mu is population and sample is x-bar

Question 7

Which is most influenced by the skew: mean, median, or mode?

Answer 7

Mean

Question 8

Measures of Variation Defined

Answer 8

The more variation in your data, the less precisely you can estimate the population’s location (e.g., mean) from the sample information.

Question 9

Measures of variation are?

Answer 9

highest score minus lowest score(ie. Data hours of day spent on phone = 3, 4, 6, 7 so 7-3 = range of 4) and sum of squared errors “sum of squares” (gives the total deviation from the mean)(take every data point and subtract from mean and then square it to get rid of negative and then add all together. Want all numbers to be positive so we can actually see a variance.)

Question 10

Range

Answer 10

(highest score minus lowest score)(ie. Data hours of day spent on phone = 3, 4, 6, 7 so 7-3 = range of 4)

Question 11

sum of squared errors “sum of squares”

Answer 11

gives the total deviation from the mean
(ie. take every data point and subtract from mean and then square it to get rid of negative and then add all together. Want all numbers to be positive so we can actually see a variance.)

Question 12

Variance

Answer 12

the average of the sum of squared deviations.
◦Is always a positive number
◦Accentuates the extreme differences

Question 13

Standard Deviation

Answer 13

the standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

Why? A measure of variance that is expressed in the same unit of measurement of the original data. Used more!

Question 14

Z-scores (or “standard scores)

Answer 14

Tell how many standard deviations a raw score is from the mean.
e.g., z = 1.96 means 1.96 SDs above the sample mean.

I.e., deviations from the mean in SD units.
Any standardized variable has a mean = 0 and SD (& variance) = 1
(Does NOT mean variable is normally distributed)

Permits a standard way to compare across scores / measures

Z scores allow us to determine probabilities.E.g., the probability of a randomly selected student passing a class.

Question 15

Null Hypothesis “significance Testing” Steps

Answer 15

Step 1: State the hypothesis.
Step 2: Set the criterion for rejecting the null hypothesis.
Step 3: Compute the test statistic.
Step 4: Decide whether to reject the null hypothesis.

Question 16

Null hypothesis Defined

Answer 16

Norelationship between variables (in population!)

Or, no difference between groups

Question 17

Alternative hypothesis (H1)

Answer 17

The null (no relationship) is not true. 
(non-directional hypothesis).

Or, there is a relationship, or difference between groups in one direction (a directional hypothesis).
E.g., “I/O is better than Clinical”

Question 18

Alpha () level (p-value)

Answer 18

probability of a Type I error (e.g., 5%).

A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e. that the null hypothesis is true).

The level of statistical significance is often expressed as a p-value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Question 19

Type I error

Answer 19

Wrongly rejecting the NULL hypotheses.
(concluding that “there is a relationship” or “two groups differ” in the population, when it just ain’t so.)
Ie. Saying a man is pregnant

Question 20

Set Criterion for Rejecting Ho

Statistical Significance

Answer 20

We decide how much risk to tolerate.

Traditional cutoff for statistical significance = .05 / .01 / .001

Question 21

Type II error:

Answer 21

Wrongly failing to reject the null hypothesis.
(Saying “no difference”/“no relationship” when there is one in the population.)
β (beta)= probability of making a Type II error
Statistical power = (1 – β).
Probability of rejecting the null hypothesis (H0) when it is false

We want an “80% chance of finding an effect, assuming there is one in the population” (power of .80)

Ie. saying a pregnant women isn’t pregnant.

Question 22

Critical value

Answer 22

indicate region of rejection:
Values (of a statistic) of the sampling distribution that are improbable if the NULL is true.
E.g., (z > 1.65) OR (z > 1.96 or < -1.96): for p-value of

Question 23

Directional H1 is a one or two tailed test?

Answer 23

one-tailed test

Question 24

Nondirectional H1 is a one or two tailed test?

Answer 24

two tailed test

Question 25

Compute test statistic

Answer 25

-Some ratio of MODEL / ERROR
(variance explained by our model / unexplained variance)e.g., z, t-ratio, f-ratio, chi square (we’ll compute these later).

-Compare test statistic value (e.g., z) to critical value.
e.g., is test statistic > 1.65?

Question 26

Correlation/regression

Answer 26

Is the relationship significantly different from zero?

Question 27

t-test/anova

Answer 27

Difference between groups greater than zero ?

Question 28

Correlation defined

Answer 28

How similar or how related your variables are. Do these variables walk together, vary in similar ways. As one increases does the other increase. Is there a relationship. An index of the linear relatedness of two variables.

Ranges between relationship -1 and +1

The sign of the correlation coefficient indicates?

• whether the relationship is positive or negative.
• Positive = as x increases, y increases. Negative = is as x increases, y decreases.

Absolute value of the coefficient indicates?

• How strong the relationship is and Pearson’s r is what we use to show that relationship.
• R value = how strong the relationship is. Between -1 and +1

Question 29

Positive Skewness

Answer 29

when the tail on the right side of the distribution is longer or fatter. The mean and median will be greater than the mode.

Question 30

Negative Skewness

Answer 30

when the tail of the left side of the distribution is longer or fatter than the tail on the right side. The mean and median will be less than the mode.

Question 31

Kurtosis

Answer 31

The measure of outliers present in the distribution.