Exam 1 in-class notes

Question 1

Population description

Answer 1

The set of all the individuals of interest in a particular study

Vary in size; often quite large

Question 2

Population notation

Answer 2

N

Question 3

Sample definition

Answer 3

A set of individuals selected from a population.

Usually intended to represent the population in a research study.

Question 4

Sample notation

Answer 4

n

Question 5

Variable

Answer 5

Characteristic or condition that changes or has different values for different individuals

Question 6

Parameter (or parameter estimate)

Answer 6

A value that describes a population

Derived from measurements of the individuals in the population

Question 7

Statistic

Answer 7

A value that describes a sample.
Derived from measurements of the individuals in the sample.
Statistics are parameter estimates.We derive a statistic because we are trying to estimate a parameter.

Question 8

Descriptive statistics goals

Answer 8

Summarize data
Organize data
Simplify data (means, tables, graphs, etc)

Question 9

Inferential statistics goals

Answer 9

Study samples to make generalizations about the population.

Interpret experimental data.

Question 10

Sampling error

Answer 10

the distance between a sample statistic and a population parameter.

Since the parameters are typically unknown we must estimate sampling error.

Question 11

Sampling error indicators

Answer 11

1) Variability. Low variability = low sampling error

2) Sample size. Large sample = low sampling error

Question 12

Constructs

Answer 12

Internal attributes or characteristics that cannot be directly observed.

Question 13

Operational definition

Answer 13

Identifies the set of operations required to measure an external (observable) behavior.

Question 14

Discrete variable

Answer 14

Has separate, indivisible categories.
No values can exist between 2 neighboring categories (i.e. cannot have 1.5 kids)

(these variable types refer to the underlying construct, not the operational definition)

Question 15

Continuous variable

Answer 15

Has an infinite number of possible values between any two observed values.

(these variable types refer to the underlying construct, not the operational definition)

Question 16

Nominal (named)

Answer 16

Labeled groups with no inherent quantitative relationship between each (e.g. diagnosed with disorder or not, restaurant options)

Question 17

Ordinal (ordered or ranked)

Answer 17

Categorized observations by size or magnitude (i.e. S, M, L, XL shirt sizes, class ranking, placement in a race)

Question 18

Interval

Answer 18

Ordered categories with equal size between categories of equal size.

Arbitrary zero point (IQ, Fahrenheit, Celsius)

Question 19

Ratio

Answer 19

Ordered categories with equal size between categories of equal size

Non arbitrary zero point (height, weight, Kelvin)

Question 20

Non-experimental (i.e. cross sectional) studies
Describe

IV
DV

Answer 20

examine associations between variables - no manipulation involved.

IV in these studies is called the Predictor variable.
DV is called the Outcome variable.

Question 21

Statistical Notation

1) IV (predictor variable) is commonly referred to as __ variable
2) DV (outcome variable) is commonly referred to as the __ variable.

Answer 21

1) X

2) Y

Question 22

N =

Answer 22

the number of scores within a population (the population size)

Question 23

n =

Answer 23

the number of scores within a sample (the sample size)

Question 24

Sigma ∑

Answer 24

defines what needs to be summed in a formula

Question 25

Order of Operations

When is ∑ done?

Answer 25

Summation is done AFTER operations in parenthesis, exponents and multiplication or division.

Summation is done BEFORE other addition or subtraction

Question 26

∑f = N

Answer 26

Meaning you sum the NUMBER of scores, not the value of those scores.

(add a pic to this slide)

Question 27

Grouping Distributions - Rules of Thumb.
1.
2.
3.
4.

Answer 27

1. Intervals should all be the same width.
2. Make the lowest score of an interval a multiple of the width (e.g. 1.0-1.9, not 1.1-2.0)
3. Use roughly 10 class intervals but use your best judgement (e.g. short report format > fewer; larger research report > more)
4. Make the interval width a relatively simple number (e.g. 1, 2, 5, 10)

Question 28

Histograms rules of thumb

Answer 28

1. X-axis lists intervals increasing from left to right, starting with 0 (unless negative scores)
2. Y-axis lists frequencies increasing from bottom to top, starting with 0 (unless negative scores)
3. Do not exclude intervals with a frequency of 0
4. Width corresponds to score’s real limits (when ungrouped; class interval when grouped)
5. Use for interval and ratio data

Question 29

When is it best to use a Histogram

Answer 29

for interval and ratio data

Question 30

Polygons

Answer 30

1. Height of the bars in a histogram are replaced by a dot in polygon graphs. Dot height = frequency.
2. Connect dots with continuous line
3. Close the polygon with lines to the Y=0 point
4. Can be adapted to grouped frequency distribution data

Question 31

When to use a bar graph

Answer 31

Nominal & ordinal data, to visualize frequency distributions

Question 32

Nominal & Ordinal Data - how to display

Answer 32

1. Bar graph instead of histogram
2. Signifies to readers the nature of the data at a glance
3. Amount of space between bars does not matter, but they should be equal

Question 33

Nominal scales

Answer 33

REMEMBER:
Nominal (named) scales have no inherent order or value associated to the score. Data sets contain numbers, and usually not names so 1 = male, 2 = female, 3 = other; or 1 = Caucasian, 2 = African American, 3 = Asian/Pacific Islander, 4 = Latino/Hispanic, etc…

The value associated with the response is fairly meaningless and only serves to make distinctions between the groups.

Question 34

Ordinal scales

Answer 34

REMEMBER:
Ordinal (ordered or ranked) scales do provide information about inherent order, but do not indicate what the distances are between the ranks. E.g., in a 100m race, the ordinal scale will tell us who finished 1st, 2nd, 3rd, etc… but this scale does not tell us how spread out or clustered together the racers were (was the person in 1st place way ahead of the rest? Or did they barely win?)

Question 35

Interval & ratio scales

Answer 35

REMEMBER:
Interval & ratio scales contain information about the intervals or “distance” between values. Specifically, that they are equal. These scales provide the most information

Question 36

Nominal data doesn’t contain much information.

1) what does it have?
2) Best way to display?

Answer 36

1) Frequency is really all we’ve got, and from that we can get proportions.
2) Bar charts (better for emphasizing frequency), Pie charts (better for emphasizing proportions)

Question 37

Bar charts with nominal data are better (than pie charts) for…

Answer 37

emphasizing frequency

Question 38

Pie charts with nominal data are better (than bar graphs) for000

Answer 38

emphasizing proportions

Question 39

Histograms vs Bar charts

Answer 39

Bar charts imply distinct categories.

Histograms imply continuous variable measurements

Question 40

Visualizing frequency distributions - 2 types

Answer 40

Symmetrical

Skewed

Question 41

Symmetrical frequency distributions

Answer 41

Each side of the distribution is a mirror image of its counterpart

Question 42

Skewed frequency distributions

Answer 42

Scores tend to pile up on one side of the distribution or the other, which creates a “tail”

Question 43

Positive skew

Answer 43

Scores pile up on the LOW end of the measure (arrow on tail points towards + side)

Question 44

Negative skew

Answer 44

Scores pile up on the HIGH end of the measure (arrow on tail points towards - side)

Question 45

Central Tendency

Answer 45

A single score (value) that best represents the center of a distribution

Question 46

µ = ∑x÷N

Answer 46

Population Frequency Distribution

Question 47

M = ∑x÷n

Answer 47

Sample Frequency Distribution

Question 48

Population Frequency Distribution Equation (Mean)

Answer 48

µ = ∑x÷N

Question 49

Sample Frequency Distribution Equation (Mean)

Answer 49

M = ∑x÷n

Question 50

Mean

Answer 50

Sum of the scores divided by the number of scores in the data.

The amount each individual receives when the total is divided equally among all the individuals in the distribution

Question 51

Median

1) What it is
2) how to calculate

Answer 51

MID.
Midpoint of the scores in a distribution when they are listed in order from smallest to largest.

It divides the distribution into two groups of equal size.

Step 1. List scores from smallest to largest
Step 2. Pick the middle score (if an odd number of scores). For even number of scores - divide the middle two values - i.e. if middle scores are 4 and 5, median would be 4.5.

Question 52

Mode

Answer 52

Which score got the MOST.

The score or category that has the greatest frequency of any score in the frequency distribution.

• Corresponds to an actual score in the distribution.
• It is possible to have more than 1 mode
• Distributions can also have none when they represent a uniform distribution.

Question 53

In a skewed distribution:

1) Mean
2) Median
3) Mode

Answer 53

1) gravitates toward the tail in a skewed distribution
2) gravitates toward the tail, but not as much as the mean
3) tends to be closer to the short tail

Question 54

If the mean - median > 0

TEST QUESTION

Answer 54

the distribution is positively skewed

Question 55

If the median - mean < 0

TEST QUESTION

Answer 55

the distribution is negatively skewed

Question 56

the distribution is positively skewed if the mean - median (greater than or less than) 0

TEST QUESTION

Answer 56

>

Question 57

the distribution is negatively skewed if the mean - median (greater than or less than) 0

TEST QUESTION

Question 58

Vector

Answer 58

?data set?