Statistical Analysis of Quantitative Data Flashcards
Purpose of Stat Analysis in Quan Research
- To describe the data (ex: sample characteristics)
- Estimate population values
- To test hypotheses
- To provide evidence regarding measurement properties of quantified variables
Levels of Measurement from Lowest to Highest
Nominal
Ordinal
Interval
Ratio
Nominal Level
Lowest level
involves using numbers simply to categorize attributes
Named
ex: eye color
Ordinal level
2nd Lowest Level
Ranks people on an attribute - hierarchy but unquantifiable - cannot know the distance betwen levels or it cant be quantified
Named and Natural Order
ex: Level of satisfaction
Interval Level
2nd highest level
Ranks people on an attribute AND specifies the distance between them - oftne used interchangeably with ratio
Named, Natural Order, and Equal distance between intervals
ex: Temperature
Ratio Level
highest level
ratio scales, unlike interval scales, have a meaningful zero and provide information about the absolute magnitude of the attribute
Named, Natural Order, Qual distance between intervals, and a “True Zero” so ratio between values can be calculated
ex: Height
Nominal = ___
Names
ex: Male = 1; Female =2 etc
Nominal Level is more like taking ____ data
qualitative
In many experiments, the independent variable is what level?
Nominal!!
Numeric Pain Scale is what level
Ordinal
Age is what level
Ratio
Hours studied for a test is what level
Ratio
Most biophysiologic data like pulse is what level
Ratio
Amount of money in bank account is what level
Ratio
What level are the following 4 things:
- Time of Day
- Completion time for running (hr/time)
- Runner registration # ina race
- Finish order for a race
- Interval (0 does not mean absence of time so its not ratio)
- Ratio
- Nominal
- Ordinal
What level is gender
nominal
What level is height wieght and pulse
ratio
What level is Grade in School
Ordinal
What level is temperature
interval
What level is zip code
nominal
What level is dates on a calendar
interval
Descriptive Statistics
Used to describe and synthesize data
Describes the data and what the sample looks like
Involves parameters and statistics
What sets parameters and statistics apart`
Parameters are descriptors for a population
Statistics is a descriptive infex from a sample
Inferential Statistics
USed to make inferences about the population base don sample data
How does descriptive and inferential statistics differ
Descriptive stats is just for the group in front of you but inferential stats makes the inferences about the generalizable population
Frequency Distribution
A systemic arrangement of numeric values on a variable from lowest to highest and a count of the number of times (and/or percentage) each value was obtained
Frequency distributions can be described in terms of what 3 things
- Shape
- Central Tendency
- Variability
In what ways can frequency distributions be presented
- In a table (Ns and percentages)
2. Graphically (ex: frequency polygons)
Frequency distributions can be described by their ____
symmetry
What is normal symmetry of a frequency distributionc alled
Normal Distribution (Bell Curve)
Skewed/Asymmetric Frequency Distribution
A distribution either skewed positively or negatively
Positive Skew
Long tails point right
ex: Income
Negative Skew
Long tails point left
ex: Youth death
Modality
number of peaks in a frequency distribution
can be unimodal, bimodal, multimodal
Unimodal
1 peak
Bimodal
2 peaks
can include normal distribution if averaging 2 peaks into a bell shaped curve
Multimodal
2+ peaks
Central Tendency
index of “typicalness” of a set of scores that comes from center of the distribution
Includes mode median and mean
Mode
Measure of central tendency that is the most frequently occurring score in a distribution
ex: 2333456789 - Mode = 3
Median
measure of central tendency where the point in a distribution above which and below which 50% of cases fall
ex: 23334|56789 - Median = 4.5
Mean
measure of central tendency that equals the sum of all the scores divided by the total number of scores
ex: 2333456789 Mean = 5
What measure of central tendency is most useful for when scores are skewed
Median
What measure of central tendency is seen msot frequently
Mean
Which measures of central tendency is least helpful and most helpful when using standard deviation
Mode - least helpful
Mean - most helpful
Why is median helpful for skewed results
because it can offset the skew
Variability
the degree to which scores in a distribution are spread out or dispersed: homogeneity v heterogeneity
Homogeneity
Little variability in a frequency distribution sample
Makes for a taller and less wide spike
Heterogeneity
Great variability in a frequency distribution sample
What are the 2 indexes of variability not seen in something like the mean
Range
Standard Deviation (SD)
Range
The highest value minus the lowest value
shows variability
can be misled by outliers
Standard Deviation (SD)
average deviation of scores in a distribution
shows variability - preferred to range
What is the Rule when it comes to standard deviations?
Rule of 68, 95, 99.7
68% of all Data/Sampling occurs within +/- 1 SD
95% of all data/sampling occurs within +/- 2 SD
99.7% of all data/sampling occurs within +/- 3 SD
What is important to know about the tails of Standard Deviation in a Normal Distribution
the 0.3% outside 3 SD means that the tails never truly touch 0 - so there is always a theoretical possibility for outliers any distance out
Bivariate Descriptive Statistics
Used for DESCRIBING the relationship between 2 variables
Approachs: Crosstabs (Contingency Table) or Correlation Coefficients
Correlation Coefficient
Describes the intensity and direction of a relationship
Rnages from -1 to 1
Negative Correlation Coefficient Relationship
-1 to 0
One variable increases in value as the other decreases
ex: amount of exercise and weight
Positive Correlation Coeffieicnt Relationship
0 to 1
Both variables increase/decrease
ex: Calorie consumption and weight
What does a correlation coefficient of 0 mean
there is no value difference / there is no relationship
The greater the absolute value of the correlation coefficient…
the stronger the relationship
ex: r=-.45 is stronger than r=.40
If there are multiple variables and you want to see all of the correlations/relationships what can be displayed
A correlation matrix
Pearson’s r
the product-moment correlation coefficient
computed with continuous measurements
r
used for Ratio level / scales