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Mod 16 Statistical Analysis
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Gravity
16.A and 16.B
Terms in this set (39)
What do using numbers help to do in regards to statistics?
-characterize and 'draw inferences'
-helps with INFORMED DECISION
Population
the group about which the investigator wants to draw conclusions
Parameters
the specific measures of the population's characteristics
Sample
the subgroup of the population 'measured'
Experimental type research
-A QUANTITATIVE UNDERSTANDING OF PHENOMENON
- data transformed to numbers
-entering numbers on computer
-use statistical manipulation of the numbers to find out info
What do numbers mean??
FIRST COLUMN - identification
SECOND/THIRD COLUMN - data inputs (Dependent variables, age, gender, etc..)
Statistical programs
summarize and transform data from numbers into meaningful information -- Researcher INTERPRETS THE RESULTS
How to select a statistic
-research question
-level of measurement (nominal, ratio, etc...)
- quality of information collected
-sampling procedures
-sample size
3 types of statistical analysis
-descriptive
-associations and relationships
-drawing inferences
Descriptive statistics
Reduce large sets of observations into more compact and interpretable forms
Frequency distribution
Reflects how frequently the value of the variable occurs
-groups the variables into categories
-can describe the frequency distribution of the data
Contingency Tables are...
Two-dimensional frequency distribution
-used with categorical data
-describes a relationship between two variables
Measures of Central Tendency
-Mean
-Median
-Mode
Measures of Variability
Indicates the degree of dispersion (range and SD)
-similar scores, little dispersion
-different scores, high dispersion
-SD tells how much scores deviate, on average, from the mean
Drawing Inferences
-generalizing from samples to whole population
-major role of statistical analysis
-accuracy of inference from sample to population depends on (representation of the sample)
What are the 5 action process steps for inferential statistics
1. State the hypothesis
2. Selecting significance level
3. Compute the calculated value
4. Obtain a critical value
5. Reject or Fail to Reject Null Hypothesis
State the Hypothesis (Step 1)
The null is a statement of no differences between or among the groups
-alternative hypothesis: expected outcome of the researcher
If you reject the null, you usually accept the alternative/research hypothesis
Selecting significance level Step 2
You want to be 95% confident, so your P-value is less than 0.05 (the smaller the p-value, the more confident outcome it is not by chance)
-want to be sure the results will be because of the DV and NOT by chance
Type 1 Error
-rejecting the null hypothesis when it is true
-may happen when the selection of the sample is compromised
-you find a difference when there should nOT be
WORSE TO HAVE TYPE 1 ERROR
Type II error
-accepting the null when it is WRONG or rejecting the alternative when it is TRUE
-researcher fials to find a difference between the two or more groups
-Not enough power to the study:
---sample size too small, effect size too small, or power of the statistics used is not enough
Step 3: compute the caluclated value
must choose and calculate a statistical formula (parametric or nonparametric procedures)
Parametric statistics
-more powerful!
-able to detect smaller differences and detect a significant difference AND decreases type II errors
Rules to use parametric statistics
-normally distributed
-homogeneity of variance
-data is at least at the interval level
Advantages of nonparametric
-tests the median instead of the mean
-when sample size is small and potentially non-normal
-cananalyze ordinal data, ranked data and outliers
-median is good when you have outliers
Common statistical tests
-T-Test: compare 2 means with one independent variable and one dependent variable
-ANOVA: compare more than 2 means, use F-value (one-way is one independent variable, two-way or three-way is 2+ independent variable)
-MANOVA: multiple analysis of variance - two or more DEPENDENT measures
Non-parametric tests
-Chi square: whether there is a relatinship between two variables (NOT a powerful test)
Step 4: obtain a critical value
Compare to the level of significance (find it in a table or a computer will tell you)
Step 5: reject or fail to reject the null hypothesis
...
Associations and Relationships
-identify relationships between variables
-based on what you know about one variable can state something else about another variable (IF THERE IS A RELATIONSHIP OR CORRELATION)
-IDENTIFY RELATIONSHIPS BETWEEN THE VARIABLES, NOT CAUSE AND EFFECT
Regression
use to predict the effect that multiple variables have on one dependent or outcome variable (finding unknown variable and predict variable)
Correlational analysis
examines the extent to which two variables are related to each other
-negative R=-0.65
-positive R=0.82
-zero R=0.06
--Pearson product-moment correlation for interval level data (continuous scale)
--Spearman rho for ordinal data (rank order)
Correlations
0-0.20 suggests a negligible correlation
0.2-0.4 is low correlation
0.4-0.6 is a moderate correlation
0.6-0.8 is a high correlation
0.8-1.00 is a very high correlation
Simple linear regression
two variables are related, linearly related, draw regression line
Multiple regression
predict value of dependent variable based on several independent variables (strength of relationships)
Logistic regression
predict probability of an event occurring based on several independent variables
Parts of a box plot
(from top of box to bottom of box)
minor outlier, largest value that is NOT an outlier, 75th pecentile, 50th percentile (median), 25th percentile, smallest value that is NOT an outlier, extreme outlier
Cofidence intervals -parameters of population
mean and confidence intervals
range of scores with specific boundaries or confidence limits that contain the means
degree of confidence is 95% or 99%
use mean and standard error of the mean to get the CI
Sensitivity
example: the proportion who are truly UNFIT to drive that are correctly labeled as UNFIT by the test
Specificity
example: the proportion who truly are FIT to drive that are correctly labeled as FIT by the test
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