Exam 1 in-class notes Flashcards
Population description
The set of all the individuals of interest in a particular study
Vary in size; often quite large
Population notation
N
Sample definition
A set of individuals selected from a population.
Usually intended to represent the population in a research study.
Sample notation
n
Variable
Characteristic or condition that changes or has different values for different individuals
Parameter (or parameter estimate)
A value that describes a population
Derived from measurements of the individuals in the population
Statistic
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.
Descriptive statistics goals
Summarize data
Organize data
Simplify data (means, tables, graphs, etc)
Inferential statistics goals
Study samples to make generalizations about the population.
Interpret experimental data.
Sampling error
the distance between a sample statistic and a population parameter.
Since the parameters are typically unknown we must estimate sampling error.
Sampling error indicators
1) Variability. Low variability = low sampling error
2) Sample size. Large sample = low sampling error
Constructs
Internal attributes or characteristics that cannot be directly observed.
Operational definition
Identifies the set of operations required to measure an external (observable) behavior.
Discrete variable
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)
Continuous variable
Has an infinite number of possible values between any two observed values.
(these variable types refer to the underlying construct, not the operational definition)
Nominal (named)
Labeled groups with no inherent quantitative relationship between each (e.g. diagnosed with disorder or not, restaurant options)
Ordinal (ordered or ranked)
Categorized observations by size or magnitude (i.e. S, M, L, XL shirt sizes, class ranking, placement in a race)
Interval
Ordered categories with equal size between categories of equal size.
Arbitrary zero point (IQ, Fahrenheit, Celsius)
Ratio
Ordered categories with equal size between categories of equal size
Non arbitrary zero point (height, weight, Kelvin)
Non-experimental (i.e. cross sectional) studies
Describe
IV
DV
examine associations between variables - no manipulation involved.
IV in these studies is called the Predictor variable.
DV is called the Outcome variable.
Statistical Notation
1) IV (predictor variable) is commonly referred to as __ variable
2) DV (outcome variable) is commonly referred to as the __ variable.
1) X
2) Y
N =
the number of scores within a population (the population size)
n =
the number of scores within a sample (the sample size)
Sigma ∑
defines what needs to be summed in a formula
Order of Operations
When is ∑ done?
Summation is done AFTER operations in parenthesis, exponents and multiplication or division.
Summation is done BEFORE other addition or subtraction
∑f = N
Meaning you sum the NUMBER of scores, not the value of those scores.
(add a pic to this slide)
Grouping Distributions - Rules of Thumb. 1. 2. 3. 4.
- Intervals should all be the same width.
- Make the lowest score of an interval a multiple of the width (e.g. 1.0-1.9, not 1.1-2.0)
- Use roughly 10 class intervals but use your best judgement (e.g. short report format > fewer; larger research report > more)
- Make the interval width a relatively simple number (e.g. 1, 2, 5, 10)
Histograms rules of thumb
- X-axis lists intervals increasing from left to right, starting with 0 (unless negative scores)
- Y-axis lists frequencies increasing from bottom to top, starting with 0 (unless negative scores)
- Do not exclude intervals with a frequency of 0
- Width corresponds to score’s real limits (when ungrouped; class interval when grouped)
- Use for interval and ratio data
When is it best to use a Histogram
for interval and ratio data
Polygons
- Height of the bars in a histogram are replaced by a dot in polygon graphs. Dot height = frequency.
- Connect dots with continuous line
- Close the polygon with lines to the Y=0 point
- Can be adapted to grouped frequency distribution data
When to use a bar graph
Nominal & ordinal data, to visualize frequency distributions
Nominal & Ordinal Data - how to display
- Bar graph instead of histogram
- Signifies to readers the nature of the data at a glance
- Amount of space between bars does not matter, but they should be equal
Nominal scales
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.
Ordinal scales
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?)
Interval & ratio scales
REMEMBER:
Interval & ratio scales contain information about the intervals or “distance” between values. Specifically, that they are equal. These scales provide the most information
Nominal data doesn’t contain much information.
1) what does it have?
2) Best way to display?
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)
Bar charts with nominal data are better (than pie charts) for…
emphasizing frequency
Pie charts with nominal data are better (than bar graphs) for000
emphasizing proportions
Histograms vs Bar charts
Bar charts imply distinct categories.
Histograms imply continuous variable measurements
Visualizing frequency distributions - 2 types
Symmetrical
Skewed
Symmetrical frequency distributions
Each side of the distribution is a mirror image of its counterpart
Skewed frequency distributions
Scores tend to pile up on one side of the distribution or the other, which creates a “tail”
Positive skew
Scores pile up on the LOW end of the measure (arrow on tail points towards + side)
Negative skew
Scores pile up on the HIGH end of the measure (arrow on tail points towards - side)
Central Tendency
A single score (value) that best represents the center of a distribution
µ = ∑x÷N
Population Frequency Distribution
M = ∑x÷n
Sample Frequency Distribution
Population Frequency Distribution Equation (Mean)
µ = ∑x÷N
Sample Frequency Distribution Equation (Mean)
M = ∑x÷n
Mean
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
Median
1) What it is
2) how to calculate
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.
Mode
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.
In a skewed distribution:
1) Mean
2) Median
3) Mode
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
If the mean - median > 0
TEST QUESTION
the distribution is positively skewed
If the median - mean < 0
TEST QUESTION
the distribution is negatively skewed
the distribution is positively skewed if the mean - median (greater than or less than) 0
TEST QUESTION
>
the distribution is negatively skewed if the mean - median (greater than or less than) 0
TEST QUESTION
Vector
?data set?
