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
Spearman’s rho
used for correlations between variables measured on an ordinal scale (lower level) as compared to pearson’s r being ratio
Clinical Decision Making in EBP involves the calculation of what ?
Risk indexes - so that decisions can be made about relative risks for alternative treatments or exposures
ex: Absolute Risk, Absolute Risk Reduction (ARR), Odds ratio (OR), Numbers needed to treat
Absolute Risk
Index used a lot in clinical decision making to decide in doing an intervention and whether there will be actual reduction of poor outcomes
Absolute Risk Reduction (ARR)
Comparing risks in the group who got the outcome and who did not -estimated proportion of those spared undesirable outcomes because of their exposure to this intervention
Odds Ratio (OR)
Odds of proportion of those with the adverse outcome relative to those without it - what are the odds experimental group v control group develop undesirable outcomes
Often seen in media/lay terms
Numbers Needed To Treat Risk Index
Estimation of how many people need to get an intervention before we see the prevention of one tru undesirable outcome
So if 3.3 people need a smoking intervention before 1 quits smoking we can take this into account for budgeting purposes
Inferential Statistics
Used to make objective decisions about population parameters using sample data
Provides a means for drawing inferences about a population, given data from a sample
ex: Taking tylenol is the assumption of the trial’s generalizations
Inferential stats is based on …
the laws of probability
Why is sampling error a big issue for inferential statistics
Because fluctuation in samples/Unrepresentative samples do not allow accurate generalizability to the greater population
A math program will assume we used best methods, but if our convenience sample under or overrepresented the population then it still runs the numbers assuming this and gives false results - this is why we should remain skeptical
Inferential statistics uses the concept of…
theoretical distributions (to the entire population)
ex: Sampling distribution of the mean error
What do the stats/sampling distributions of inferential samplings act as a proxy for
Since we do not have the time or means to do infinite sampling we can assume principles of stats to assume what the general population mean would be
Inferential statistics always assumes that the population is…
normally distributed
What is the standard deviation called in inferential statistics
Standard Error of the Mean (SEM)
So the SE is estimated from the SE of the actual sample
The ____ the SEM the better the generalizability
smaller
What improves accuracy of the estimate and shrinks SEM
larger sample size
alpha represents…
threshold of risk (5% chance for error and chance of being outside the 95% SE)
Why is it important to not udner/over represent in sampling as it impacts SEM
because we can end up in the tails of the distribution without knowing it
sometimes it is not our fault but we have to prevent the times it is
Alpha states there is a 5% risk…
that our results came from the chance the null hypothesis is true
2 Purposes of Inferential Statistics
Point Estimation / Interval estimation
Hypothesis Testing
Point Estimation
a single descriptive statistic that estimates the population value
ex: a mean, percentage, or OR
ex: mean BP, mean score on a scale, etc
Interval Estimation
a range of values within which a population value probably lies
involes computing a confidence interval (CI)
Confidence INtervals reflect…
how much risk of being wrong researchers take in interval estimation
Confidence Intervals
indicate the upper and lower confidence limits and the probability that the population value is between those limits
Confidence Limit is the estimate for a population range
What are the 2 main confidence interval numbers seen
99%
95%
What does a 95% CI of 40-50 for a sample mean of 45 indicate
that there is a 95% probability that the population mean is between 40 and 50
How do 95% and 99% CI differ
95% = tighter parameters but less confident, allows for a more accurate estimate
99% = less risk and less tolerance for risk, but naturally means estimate is not as precise
Hypothesis testing helps researchers…
to make objective decisions about whether results are likely to reflect chance differences or hypothesize effects
We can only ever ___ or ___ the ___ hypothesis with statistical decisions from hypothesis testing
accept or reject the null hypothesis
never proven or accepting the research hypothesis
Decisions of hypothesis is always made regarding which hypothesis
the null (accept or reject)
Rejecting the null implies..
there is a difference large enough between groups to say they are different from intervention rather than just general differences between the groups
If the value of the test statistic indicates that the null hypothesis is improbable then…
results are statistially significant
Nonsignificant results mean…
that any observed difference or relationship could have happened by chance
Statistical decisions (sig or not) are either ___ or ____
correct or incorrect
When can we know if a stat decision was correct or not
Not in the initial research but rather after enough replication
Type I Error
” False Positive “
Rejection of the null when it should not be rejected - thought we saw something when there was not
Any stat decision in an initial trial has some level/risk of…
type I or II error
Telling a man he is pregnant would be what type of error
Type I Error
Risk of Type I and II error is controlled by …
the level of significance (Alpha)
ex: Alpha = 0.05 or 0.01
alpha is usually ____
0.05
the probability of rejecting the null hypothesis when it is true - if your p value is less than the alpha you reject the null
Type II Error
“False Negative”
Failure to reject a null hypothesis when it should be rejected
Telling a pregnant woman she is not pregnant is what error
Type 2 -false negative
A type 1 error can only occur..
with statistically significant results
Power
the ability of a test to detect true relationships
increases with larger samples –> larger power
Power needs to be at least…
0.80
Does Type I and II error mean an error was made necessarily?
No it means there was risk for making that error based on the conclusion
Hypothesis Testing Procedure
- Select an appropriate Stat Test
- Specify level of significance (ex: alpha = 0.05)
- Compute a test statistic with actual data
- Determine Degrees of Freedom (df) for the test stat (made by program)
- Compare computed test stat to a theoretical value - decide if significant or not
Important Bivariate Stat Tests
t tests
ANOVA
chi squared test
correlation coefficients
effect size indexes
t-test
tests the difference between 2 means
2 types: independent groups between subjects and dependent (paired) groups within subjects
t test for independent groups: between subjects test
tests difference of means for 2 independent groups
ex: men and women
IV is nominal
DV is continuous
t test for paired groups: within subjects test
to test the difference of means of a paired group
ex: pretest v post test for same people
IV is nominal
DV is continuous
p-value
probability of the difference between the means meaning the null hypothesis is true
So there is a 0.1(1%) chance that the difference in means is explained due to regular normal variation
alpha v p-value
Alpah is a 5% risk for error, but the p value is a 1% cahnce that the difference is from regular error
if the p value is smaller than the alpha you can reject the null hypothesis
error does not mean mistake ehre it means there is normal distribution - opposite of bias
ANOVA (Analysis of Variance)
Tests the difference between more than 2 means (3+ independent groups)
IV - Nominal
DV - continuous
Can be one way (3 groups) Multifactor/Two Way, or Repeated measures ANOVA (within subjects)
What does ANOVA sort out
the variability of an outcome variable into 2 components:
- variability due to the IV
- Variability due to all other sources
ex: Variation between groups is contrasted with variation within groups
What is the statistic yielded with ANOVA
F Ratio Statistics (it is the variation between groups contrasted wiht the variation within groups)
Chi Squared Test
Tests the difference in proprotions in 2+ independent groups
Uses a contingency table - comparing observed frequencies in each cells with expected frequencies (the frequencies expected if there was no relationship)
IV - Nominal (or ordinal)
DV - NOMINAL!!! (or ordinal in some)
Chi Squared Tests are the inferential statistics version of a…
crosstab table
Test stat for Chi Squared Tests
X^2
What are test statistics
values used to compare in a table to get the p value - not used much anymore
If p is lower than the alpha..
results are statistically significant
Correlation Coefficients can be used in both…
inferential and descriptive statistics
IV and DV -Continuous
What are the 3 things needed for any inferential statistic test
Test Statistic Number
P Value
Degrees of Freedom (DF)
could also include effect size
Effect Size Indexes
summarize the magnitude of the effect of the IV on the DV - how much effect on the outcome measured
an important concept in power analysis
In a comparison of two group means (ex. in a t test situation) the effect size is represented by…
Cohen’s d
d < or equal to .20 means…
small effect
d = 0.50 means…
moderate effect
d > or equal to .80 means…
large effect
Multivariate Stat Analysis
stat procedure for analyzing relationships among 3 or more variables simultaneously
ex: Multiple regression, ANCOVA, logisitc regression
Multiple Regression
used to predict a DV based on 2 or more IV (predictors)
IV - continuous (interval or ratio) or dichotomous
DV - continuous (interval or ratio level data)
ex: What are things that effect birth weight: Grams at Birth - what is the number of IVs determining that
ex: maternal age, income in dollars, maternal weight, SBP, smoking etc
What is the stat used in multiple regression
the Multiple Correlation Coefficient symbolized as R
Multiple Correlation Coeffiicient (R)
The correlation index for a DV and more than 2 IVs represented by R
does not have negative values, but shows strength of relationships - not direction
R sees ___ not ___
strength not direction
R^2
an estimate of the proportion of variability in the DV accounted for by all predictors (multiple regression)
ANCOVA (Analysis of Covariance)
Extends ANOVA by removing the effect of confounding variables (covariates) before testing whether mean group differences are stat significant
IV - Nominal (group status)
Covariates - cont./dichotomous
Individual differences variability due to all other sources
Logistic Regression
analyzes relationships between a nominal-level DV and more than 2 IVs
yields an ODDS RATIO - the risk of an outcome occurring given one condition versus the risk of it occurring given a different condition
Reliability Assessment Tests
Test Retest Reliability
Interrater Reliability
Internal Consistency Reliability
Validity Assessment Tests
Content Validity
Construct Validity
Criterion Validity
Reliability
Accuracy of Results
Test Retest Relaibility
Give the same test over and over and hope to see similar results in that person
Interrater Reliability
Extent at which 2 raters will assign the same score to some attribute
Internal Consistency Reliability
Extent to which various components all measure the same thing -ex: chrombeck alpha
Content Validity
Multiple item scales whether content measures constructs of interest
Criterion Validity
How consistent with measurements on a scale with a comparison to a gold standard criterion
Sensitivity and Specificity
Sensitivity
ability to correctly ID a case
Specificity
Ability to correctly rule out certain cases
Construct Validity
Extent to which measurement really measures the true construct
done via hypothesis testing
When reading a research article and its hypothesis testing, what things are important to look for
- The Test Used
- The value of the calculated statistic
- Degrees of freedom
- Level of statistical significance (p-value)
A researcher measures the wieght of people in a study involving obesity and Type 2 diabetes. What type of measurement is being employed?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
D. Ratio
Rationale: Many physical measures, such as a person’s weight, are ratio measures. Gender is an example of a nominally measured variable. A measurement of ability to perform ADLs is an example of ordinal measurement, and interval measurement occurs when researchers can rank people on an attribute and specify the distance between them, e.g., psychological testing.
T/F: A bell shaped Curve is also called a normal distribution
True
Rationale: A special distribution called the normal distribution (a bell shaped curve) is symmetric, unimodal, and not very peaked
The researcher subtracts the lowest value of data from the highest value of data to obtain:
A. Mode
B. Median
C. Mean
D. Range
D. Range
Rationale: The range is calculated by subtracting the lowest value of data from the highest value of data. The mode refers to the most frequently occurring score. The median refers to the point distribution above which and below which 50% of the cases fall. The mean is the sum of all the scores divided by the total number of scores.
T/F: A correlation coefficient of -.38 is stronger than a correlation coefficient of +.32
True
Rationale: For a correlation coefficient, the greater the absolute value of the coefficient, the stronger the relationship. So, the absolute value of −.38 is greater than the absolute value of +.32 and thus is stronger.
Which test would be used to compare the observed frequencies with expected frequencies within a cotningency table?
A. Pearson’s r
B. Chi squared test
C. t test
D. ANOVA
B. Chi Squared Test
Rationale: The chi-squared test evaluates the difference in proportions in categories within a contingency table, comparing the observed frequencies with the expected frequencies. Pearson’s r tests that the relationship between two variables is not zero. The t-test evaluates the difference between two means. The ANOVA tests the difference between more than two means.
