Unit 8 Flashcards
Deductive Research Paradigm
- Deductive approach
- top-down (large to small)
- Theory-hypothesis-test hypothesis-specific answer
- requires statistics to interpret large amounts of data (quantitative)
Inductive Research Paradigm
- Inductive approach
- Bottom-up (small to large)
- Generalize-analysis-data
- generally fluid, qualitative approach
- “research in ABA is typically inductive but also quantitative
Descriptive Statistics
the goal of descriptive statistics is to describe properties of the sample you are working with
- central tendency
- variability
- effect size
Reasons to Use Descriptive Statistics in ABA:
- complement visual analysis
- Program Evaluation
- We use Descriptive Statistics already (level change and IOA)
- May help gather funding
Reasons to not Use Descriptive Statistics in ABA:
-may hide trends
Inferential Statistics
- the goal of inferential statistics is to use sample data as the basis for answering questions about the population
- since we rely on samples, we must better understand how they relate to populations (use hypothesis testing to reach that goal-T-tests, ANOVA)
Reasons for using Inferential Statistics in ABA:
- appropriate for certain types of research
- may open doors for funding
- perceived weakness of reliance on visual analysis in ABA
Reasons for not using Inferential Statistics in ABA:
- don’t tell us how likely the results are to be replicated
- don’t tell us the probability that the results were due to chance
- the probability is a conditional probability
- best way to increase your chances of significance is increasing number of participants
- large number of variables that will have very small effects become important
- limits the reasons for doing experiments
- reduce scientific responsibility
- emphasize population parameters at the expense of bx
- “behavior is something an individual does, not what a group average does”
- *we should be attending to:
- value/social significance
- durability of changes
- number and characteristics of participants that improve in a socially significant manner
One reason for using descriptive statistics in ABA is that they:
Complement visual analysis
Inferential statistics involve decisions about ______levels of data
Inferential statistics involve decisions about ORGANISM levels of data
A focus on inferential statistics may take the focus away from:
Socially significant results
Four types of Data:
- Nominal (name)
- Ordinal (order)
- Interval
- Ratio
Nominal Data
(name)
- refers to categories
- examples: school districts, colors
Ordinal Data
(order)
- quantities that have an order
- examples: first place/second/third, pain scale
Interval Data
- difference between each value is even
- never a True Zero
- Examples: degrees Fahrenheit
Ratio Data
- difference between each value is even
- has a True Zero
- Examples: time, weight, SIB
Three measures of central tendency?
- Mean
- Median
- Mode
Mean
- the sum of the scores divided by the number of scores
- advantage of the mean: every number in the distribution is used in its calculation
- most preferred measure
Median
- score that divides the distribution exactly in half
- Median split: gives researchers two groups of equal sizes: low scores/high scores
- middle score
When to use the median:
- extreme scores/skewed distributions
- undetermined values
- open-ended distributions
Mode
- score or category that has the greatest frequency (the peak)
- A distribution can have more than one mode
1. Bimodal: two modes/peaks, these can be equal or major/minor
2. Multimodal: more than two modes - Easy to find in basic frequency distribution tables
- the mode is NOT a frequency-it is a score/category
When to use the mode
- it can be used in place of or in conjunction with other measures of central tendency
1. Nominal scales: only measure of central tendency for nominal scales
2. Discrete variables: what is “most typical” the goal of measure of central tendency
3. Describing shape: easy to figure out
What is the most representative method of reporting central tendency in your data when you have extreme scores?
median
The most common method of reporting central tendency is
mean
The mode is an ideal measure of central tendency for
nominal variables
The median is an ideal measure of central tendency for
- extreme scores/skewed distributions
- undetermined values
- open-ended distributions
Variability
-provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together
Three measures of variability
- range
- interquartile range
- standard deviation
Range
- simply the distance between the largest score and the smallest score +1
- crude and unreliable measure of variability: does not consider all the scores in the distribution
Standard Deviation
- most important measure of variability
- measures the typical distance from the mean
- uses all the scores in the distribution
Standard Deviation in ABA:
- can be used to identify variability
- can be described to identify important variability in IOA data
The standard deviation measure can reveal important patterns in
IOA data (inter-observer agreement data)
The standard deviation measure describes the typical distance from the
mean
Probability
-the relationship between samples and populations are usually defined in terms of probability
2 Kinds of Probability
- Subjective
2. Objective
Subjective Probability
-based on experience or intuition (chance of rain, likelihood of recession)
Objective Probability
-based on mathematical concepts and theory
Probability Formula
P(event)= # of outcomes classified as the event/total # of possible outcomes
Random Sampling
- inorder to apply rules of probability to samples and populations we must satisfy two requirements
1. each individual in the population must have an equal chance of being selected
2. if more than one individual is to be selected for the sample, there must be constant probability for each every selection - sampling with replacement
Probability and proportion are equivalent
-whenever a population is presented in a frequency distribution graph, it will be possible to represent probabilities as proportions of the graph
Probability and Normal Distribution
Normal shaped distributions are the most common occurring shape for population distributions
Z-Score Review
- collecting enough data tends to yield a normal distribution
- a Z-score of 1.0 means I did better than 84% of the population
We use _______ data to make inferences about populations.
We use SAMPLE data to make inferences about populations.
When establishing probabilities of outcomes, we assume random sampling with:
replacement
A normal distribution is
Both symmetrical and bell-shaped
Sampling error?
- there is a discrepancy, or amount of error, between a sample statistic and its corresponding population parameter
- samples will be different from the population
Distribution of Sample Means
- the collection of sample means for all the possible random samples of a particular size (n), that can be obtained from a population
- different samples taken from the same population will yield different statistics
- in most cases, it is possible to obtain thousands of different samples from one population
- the sample means tend to pile up around the population mean
- the distribution of sample means is approximately normal in shape
- we can use the distribution of sample means to answer probability questions about the sample means
The Central Limit Theorem
-for any population the distribution of sample means will approach a normal distribution as n approaches infinity
Distribution of Sample Means
-the shape of the distribution of sample means will be almost perfectly normal if either one of the following conditions is satisfied:
1. population from which sample selected is normal
2. The number of scores (n) in each sample is relatively large (n>30)
(also a sample mean is expected to be near its population mean)
The Law of Large Numbers
- states that the larger the sample size the more probable it is that the sample mean will be close to the population mean
- primary use of a distribution of sample means is to find the probability associated with any specific sample
Hypothesis Testing
Definition: a statistical method that uses sample data (statistics) to evaluate a hypothesis (question) about a population parameter
-basic, common inferential procedure: uses Z-scores, probability, and the distribution of sample means
Purpose: to help researchers differentiate between real patterns in data and random patterns in data
4 Main Steps of Hypothesis Testing
- State the hypothesis about a population
- Set the criteria for a decision (use the hypothesis to predict the characteristics that the sample should have)
- Collect data and compute sample statistics (obtain a random sample and compute the mean)
- Make a decision (compare the obtained sample data with the prediction that was made from the hypothesis)
Assumptions for Hypothesis Tests with Z-Score:
- random sampling
- independent observations
- the value of SD is unchanged by the treatment
- normal sampling distribution
An assumptions for hypothesis tests with -score is
random sampling
When we set a (alpha) at .05, we are ___ % sure that we are not making a decision error when we reject Ho (null hypothesis):
95%
Type I Error in Hypothesis Testing
- rejecting the null hypothesis when it is actually true
- consequences: false reports in the scientific literature
Type II Error in Hypothesis Testing
-failing to reject the null hypothesis when it is actually false
Problem with Z-scores:
- Z-scores have a shortcoming as an inferential statistic: the computation requires knowing the population standard deviation (know Zee/the population)
- therefore, we use the T-statistic rather than the Z-score for hypothesis testing
T-Test
- with a sufficient sample from a population, and independent observations we can test a hypothesis (the occurrence of the first event has no effect on the probability of the second event)
- a test used to compare two means
- usually satisfied by using random samples
- T-test is appropriate when you have 2 groups (e.g. treatment vs. control)
Advantages of Related-Samples Studies
Major advantage: eliminate the problem of individual differences between subjects. For this reason, they are called within-subject designs
-reduces sample variance, which can be inflated due to differences between subjects that have nothing to do with treatment effects
Drawbacks of Related-Samples Designs
Two types of contaminating factors that can cause D to be statistically significant when there is actually no difference between the before and after conditions are:
- Carryover effects: subject’s response in the second treatment is altered by lingering aftereffects from the first treatment
- Progressive error: subject’s performance changes consistently over time
2 Ways to deal with potential problems with related-samples designs
- Counterbalance the order of treatment presentation
2. if substantial contamination expected, us a different experimental design (i.e. independent measures)
Assumptions of the Related-Samples T-Test
- the observations within each treatment condition must be independent
- the population distribution of difference scores (D values) must be normal
ANOVA stands for?
Analysis of Variance
Definition of ANOVA
-an ANOVA would tell us whether or not there is a significant difference between three or more groups
Definition of Correlation
a statistical technique used to measure and describe a relationship between two variables Characteristics: -involves no manipulation or control -requires two scores for each individual -presented graphically in a scatter plot
What does correlation measure?
- Direction (positive vs. negative correlation)
- Form of relationship
- Degree (strength) of the relationship
-.93 is a ____ correlation.
-.93 is a STRONG correlation.
Regression
- describes linear relationship between 2 or more variables
- linear regression equation (mostly a prediction formula)
- builds upon correlations to make predicitons
Effect Size
- a measure of strength of a phenomenon
- significance testing only informs us of “the probability of obtaining the results that were obtained in the study, given that the null hypothesis is true”
What is the most acceptable effect size for a T-test?
.4 (larger the better)
Effect size is best conceptualized as
strength of a phenomenon
