Quantitative Inquiry 2

Mean (also known as arithmetic average)

'M' is the most sensitive measure of center b/c it takes into account all score in a distribution when calculated. The average of the scores its value is directly affected by the magnitude of each score in the distribution Influenced by outliers, + or -skew distribution can greatly impact the mean, so sometimes may be more useful to use Median as it is less affected by skew 42, 43, 51, 56, 56, 58, 63, 64, 65, 66, 66, 67,

Histogram

'bars' touch! Not the exact same as bar graph, resembles bar graphs, with each bar representing a class, however touching bars indicate that there are no gaps between adjacent classes. , the Y-AXIS REPRESENTS A FREQUENCY, bar graphs y-axis typically represents a mean score

What would be the advantages and disadvantages for conducting a ABAB design?

(below) multiple levels of the independent variable, if these levels represent quantitative differences, the design is said to be parametric

Nested Designs are

(combined Between- and Within-Subjects Designs): different from a factorial design because not all levels of 1 IV are exposed to another

Phi Coefficient

- BOTH variables are dichotomous (1s and 0s)

Factorial Designs: incorporating 2 or more IVs in a single experiment.

- It might be easier to think of splitting your group into more specific groups to answer more questions. - You want to see if hyperbaric oxygen therapy (HBOT) improves IQ scores - If you had 3 groups who received 3 amounts of oxygen in the hyperbaric chamber and tested them on a brief intelligence test after treatment. - Group 1 = 21% oxygen then took IQ test - Group 2 = 60% oxygen then took IQ test - Group 3 = 100% oxygen then took IQ test - This would be a 1 x 3 design. - But before you randomly split up your subjects into groups, you read that boys and girls respond differently to HBOT so you should split them up - Now you'd have 6 groups: - Group 1 = girls, 21% oxygen then took IQ test - Group 2 = girls, 60% oxygen then took IQ test - Group 3 = girls, 100% oxygen then took IQ test - Group 4 = boys, 21% oxygen then took IQ test - Group 5 = boys, 60% oxygen then took IQ test - Group 6 = boys, 100% oxygen then took IQ test - This would be a 2 x 3 design - But just before you randomly split up your subjects into those groups, you read that blood types that contain A (i.e., type A and AB) respond differently than those that don't (i.e., type B and O), so you should split them up some more to account for that - Now you'd have 12 groups: - Group 1 = contain A, girls, 21% oxygen then took IQ test - Group 2 = contain A, girls, 60% oxygen then took IQ test - Group 3 = contain A, girls, 100% oxygen then took IQ test - Group 4 = contain A, boys, 21% oxygen then took IQ test - etc. . . . . . This would be a 2 x 2 x 3 design

Advantages of Within-Subjects Designs (Within Groups; Repeated Measures)

- Much of the error variance (e.g., the differences between subjects) is controlled for because each person is compared to himself, which increases the statistical power. - You also need less subjects OR the same number of subjects increases your power.

Linear Regression and Prediction

- allows you to predict one variable's score based on knowledge of the values of others - uses a regression line - bivariate regression and multiple regression

Dynamic Designs

- assesses changes in pattern or variability - lacks discrete values of the IV that serve to distinguish the baseline & intervention phases of the baseline design - the IV is the 'disturbance '

Single-Subject Design Advantages

- avoids use of inferential statistics - repeated observations and treatments allow momentary variability to average out - it's easier to control for confounding variables (e.g., changes in diet, sleep) - error variance (pre-existing differences between groups) is eliminated - individual differences can be detected better than between and within - less subjects - allows for more "intrusive" interventions - causal relationships are easier to determine (association, directionality, isolation)

Spearman Rank-Order Correlation or (rho)

- data is ordinal, used either when your data are scaled on an ordinal scale or when you want to determine whether the relationship between variables is monotonic - can be used with nonlinear, but monotonic (no values repeated, curve never doubles-back)

Single-Subject Design Characteristics

- doesn't have to be a single subject - scores of subjects aren't averaged as in between- and within-subject designs

Examples of split-plot designs

- each plot received a different pesticide - each subplot within each plot received a different fertilizer - so subplots within a plot all received one level of a treatment IV, but different levels of another treatment IV - how is it different from our previous within-subjects factorial designs? - gender, age, blood type, pesticides, & fertilizers are all considered IVs - however, some are existing characteristics (quasi-independent variables; QIV) and some are variables that can be exposed/received ("treatments" or "true independent variables")

Disadvantage to using nested designs

- lose the ability to check for interaction effects

Single-Subject Design

- much more systematic than the case study; consists of repeated, multiple observations including multimodal assessment - are conducted with clearly defined variables - uses data that's planned before the beginning of collection - collects data throughout, including outcome - involves comparisons of some sort

Point-Biserial Correlation

- one variable is on a nominal scale, one variable is nominal while other is interval - dummy code nominal variables, run Pearson r

Discrete Trial Designs

- responds to anticipatory responding which can occur with the multiple/continuous assessments in a baseline (e.g., signal detection). - treatment conditions are randomized in presentation - ex: AABABBABABBAABBBABAABAABABBAAB - results can be presented as 1. a comparison between averaged baseline scores and treatment scores: A = 4.35, B = 5.67 2. plotting baseline scores in order first, then plotting treatment scores: AAAAAAAAAAAAAAAABBBBBBBBBBBBBBBB

Experimental vs. Quasi-Experimental Designs

- the only difference is the random assignment to groups - quasi-experimental designs typically have pre-existing groups, this can be a drawback

Equivalent Time Samples Design

- treatment conditions are administered repeatedly (e.g., caffeine and memory scores) - O1 - X1 - O2 - Xo - X1 - O3 - Xo - O4 - X1 - O5 - Xo - O6 . . .

Combining Correlational and Experimental Designs section allows:

- understand that if there is another variable that you believe could affect the relationships/differences discovered, you can account for that by including that variable as a covariate (if it is continuous) or as a Quasi-independent Variable (QIV) in your factorial design.

Disadvantages of Within-Subjects Designs (Within Groups; Repeated Measures)

-more demanding on subjects, especially if you have many levels of the IV -carryover effects: learning, fatigue, habituation (gunshots), sensitization (the entry of the experimenter alone can increase anxiety), contrast (initially high pay for responding), adaptation (dark, stench, heat). - addressing carryover effects: 1. avoiding them (e.g., fatigue), 2. counterbalancing, 3. doing both, 4. making order an IV and splitting groups

When to use nested designs

-often used when there are many levels of an IV (e.g., 9), less access to subjects, cluster sampling

What is the difference with between-subjects, within-subjects, and single subject?

1. Between-subjects: groups of subjects are randomly assigned to the levels of the IV 2. Within-subjects: a single group of subjects is exposed to all levels of the IV 3. Single-subject: subjects are exposed to all levels of the IV but the data is not averaged.

Managing Files include:

1. Original File 2. Sanitized (delete columns with names, addresses, etc.) 3. Convenient (manipulated) Files Ex: a. only data (columns) you're using in your primary analysis b. scores averaged (grouped data) c. scores sorted and blocked according to a variable

Between-Subjects Designs (Between Groups) types

1. Randomized Group Designs (i.e., Two-Group, Multigroup): randomly assign subjects to the levels of IV to form "groups" ​a. Two-Group: Subjects randomly split into 2 groups with each group receiving 1 level of the IV. Compare the means of the 2 groups. The advantage is that it is simple and less subjects are necessary. The disadvantages are that we limit the information gleaned, and when there are large differences between subjects initially, we are still not certain why the groups differ. Do not learn about the nature of the relationship, or function. ​b. Multigroup: Same, but with more than 2 groups. The advantage is that it gives us more info (testing more levels of the IV). 2. Matched-Groups Designs (i.e., Matched-Pairs, Matched-Multigroup) ​- Your subjects are matched according to their scores on a specific variable (on the pretest DV, on a variable that might affect results such as gender or education). Then matches are divided/ split into groups where each of the matched subjects goes into a different group.

Solutions to manage error variance

1. Reducing Error Variance ​- Minimize the extraneous variables (reduce distractions, personnel) ​- Keep extraneous variables constant (same instructions, experimenter, room, etc.) ​- Match subjects (reduce/match preexisting differences); example: same aged participants ​​ex: Before splitting subjects into groups, assess their symptomotology. Then, match and split, so the end result is ​​​two groups with essentially the same levels of symptomotology. This reduces external validity 2. Increasing affect of the IV ​- Make sure IV creates distinct effects (e.g., dosages, therapy is intensive) ​- Make sure DV is sensitive enough 3. Randomizing the Error Variance ​- We don't know much of the variables that contribute to error. Through random assignment, we randomly share those ​unknown variables to "even it out". 4. Statistical Analysis; estimate the probability with which error variance alone would produce differences between groups at least as large as those actually observed *use inferential statistics ​- Use probability (that's the α from the video) and inferential statistics ​

When to use Within-Subjects Designs

1. Subject variables are correlated with the DV: (hard to tell usually what those variables are). 2. Economizing subjects: you don't have access to too many 3. Assessing effects of increasing exposure on a behavior: (you want carryover effects)

Problems with expanding too much? for example of the blood type

1. You'll need more subjects 2. Interaction effects Interaction effects -Go back to before we looked at blood type.

Standard Error of Estimate

= the error in predicting Y from X, using the difference in values from the predicted Y and the actual Y.

Main effect

= the separate effect of each independent variable; the significant difference in means for any of your IVs (i.e., gender, O2 level) - if there was a main effect, there would be a difference in scores between the gender rows, or the O2 columns.

Interaction

=is present when the effect of one independent variable changes across the levels of another IV; in other words: the effects of one IV changes across levels of another IV. - the best way to look at this is with a graph. (it'll look like a cross on a line graph) - the more levels and IVs you have, the more difficult it is to determine interaction effects.

Variance (s2)

Average squared deviation from the mean. - The primary purpose is for statistical techniques - Doesn't provide much information to us because of its unit of measurement; its expressed in units of different from those of the summarized data; can be converted into a measure of spread expressed in the SAME unit of measurement as the original scores: the standard deviation

If the y-axis represents mean, this graph is most likely a _____.

Bar graph

______ presents data as bars extending away from the axis representing your IV. Best method of graphing when your IV is categorical or qualitative e.g., categories representing grades on an exam

Bar graph

If you want to address the specific questions that you had in mind when you designed your study. You most likely use _______.

Descriptive statistics

Interrupted Time Series Design

Example of Quasi experimental designs - same, but the IV is naturally occurring (i.e., not manipulated by you) - chart the changes in behavior as a function of naturally occurring event (natural disaster) rather than manipulate an IV - the naturally occurring event is the quasi-independent variable

The search to help you discover important hidden patterns in your data that may shed additional light on the problems you are interested in solving is referred to as ____.

Exploratory data analysis (EDA)

________ consists of a set of mutually exclusive categories (classes) into which you sort the actual values observed in your data, together with a count of the number of data values falling into each category (frequencies).

Frequency Distribution

Solomon four-group design:

Group 1 Pretest Treatment Posttest Group 2 Pretest Posttest Group 3 Treatment Posttest Group 4 Posttest Time→→→→→→→→→→→→→→→→ Group 1 & 2 are identical to two-group design (btwn group); 2 group testing sensitization (carryover effects) of the pretest (1 with tx and posttest and 1 with Posttest only)

If the y-axis represents frequency, this graph is mostly likely a _____.

Histogram

_____ are used to infer a characteristic of a population based on certain properties of a sample.

Inferential Statistics

Mode

Most frequent score in distribution EX: 1, 2, 4, 6, 4, 3 Mode: 4 The highest response category (the highest point on a histogram) doesn't tell you much

Example of Within-Subjects Designs (Within Groups; Repeated Measures)

O = observation/assessment, X1 = 0 caffeine, X2 = 12mg caffeine, X3 = 25 mg caffeine, X4 = 50 mg caffeine O X1 O X2 O X3 O X4 O O X2 O X3 O X4 O X1 O O X3 O X4 O X1 O X2 O O X4 O X1 O X2 O X3 O O X1 O X2 O X3 O X4 O O X2 O X3 O X4 O X1 O O X3 O X4 O X1 O X2 O O X4 O X1 O X2 O X3 O

A statistic that makes assumptions about the nature of an underlying population (normal distribution; continuous data).

Parametric Statistic:

____ is good way to represent proportions or percentages in data

Pie graph

Solving Inappropriate Baseline Levels (even if all subjects show similar baseline levels during the baseline phase, the particular levels obtained may not be useful for evaluating the effect of manipulation (ceiling/floor effects)

Solution = change your scale, manipulate variables

What is the most popular measure of spread?

Standard deviation

Interquartile Range

The middle 50% of scores (the box part of the box plot) 1) order the scores in your distribution 2) divide the distribution into 4 equal parts (quarters) 3) find the score separating the lower 25% of the distribution (Q3). The interquartile range is equal to Q3 minus Q1. Less sensitive to effects of extreme scores

Standard Deviation

The square root of the variance - Provides us useful information because it is in the same unit of measurement - Most popular measure of spread - Also sensitive to outliers

Disadvantages to Between-Subjects Designs (Between Groups)

We could choose wrong, statistical techniques are less powerful, more time with pretest. If you have many groups, it is more difficult to "match" exactly

Cohort-sequential Design:

a Developmental Designs: combines the two developmental designs and lets you evaluate them

Cross-sectional design

a Developmental Designs: create groups of participants who differ on a variable of interest but share similarities such as SES, education etc..

Longitudinal Design:

a Developmental Designs: single group of participants is followed over some time period

Another name of the horizontal axis is

abscissa or x-axis (independent variable)

Covariate:

additional correlation variable suspected to affect discovered relationship

Descriptive statistics allows

allow you to summarize the properties of an entire distribution of scores w/ just a few numbers;Need to look at descriptive statistics first then inferential stats

A solution for unrecoverable or Partially Recoverable Baselines (if baseline levels of performance cannot be recovered during reversal) caused by carryover:

change design to AB/multiple baseline/counterbalanced, minimize carryover, add subjects

Mixed Designs are also called

combined Between- and Within-Subjects Designs; sometimes called split-plot (but usually only in stats text books)

Quasi-Independent Variable

correlational variable that resembles an independent variable in an experiment

What is a solution to problems with Drifting Baselines ('impossible' to stabilize a baseline against slow, systemic changes):

display trend across intervention phases

Nonparametric Statistic

do not have those assumptions of parametric and smaller samples

Providing a number to a non-numeric item (e.g., yes = 1, no = 2) assignment of numbers to the levels of a qualitative IV (1=low, 2=moderate, 3=high) is mostly called

dummy coding

Time Series Design

example of Quasi-Experimental Designs - several observations/assessments are taken before and after your IV - can mix (between and within) and add a control group - advantages: excellent for trending data (DVs that naturally change over time) - problems: history, equal lags (i.e., equal spaces of time between assessments)

advantages to Between-Subjects Designs (Between Groups)

fewer subjects needed (if we split gender then by IV, the group would be split into 4 groups vs. 2), we account for much of the error variance, avoid carryover effects (which occur in within-subject designs) by controlling for subject variables

Classes may consist of response categories (e.g., democrat, republican, independent..) or ranges of score values ALONG a quantitative scale like IQ 65-74, 75-84, 85-94...etc. are examples of ___.

frequency Distribution

Measure of Center (also known as a measure of central tendency)

gives you a single score that represents the general magnitude of scores in a distribution

Nonequivalent control group design

include a time series component along with a control group that is not exposed to the treatment

Pretest-Posttest

includes pretest on dependent measure before Tx & posttest after introduction of treatment

What would be the advantages and disadvantages for conducting a ABA design?

includes reversal phase; baseline reassessment helps determine if the TX indeed resulted in the changes observed, fails to establish the recoverability of the baseline ^ABA designs may be appropriate if it is desirable to return the subject to preexperimental conditions prior to the termination of the study

Normal distribution

is symmetric and hill shaped; Bell Curve

median

is the middle score in an ordered distribution order you scores from lowest to highest, find the middle, with even scores, find the two middle then average tells you more than Mode, still insensitive b/c it doesn't take into account the magnitudes of the scores above and below the median. Used when the mean isn't a good choice

Discrete Trial Designs

like the baseline designs, discrete trial designs focus on the behavior of the individual participant (e.g., your air traffic controller) rather than on group behavior. Both rigidly control for variance, HOWEVER the discrete trials design DOES NOT produce a continuous within-treatment baseline that can be adjusted & fine tuned. ** behavior measured over a series of discrete trials must be averaged to provide relatively stable indices of behavior under the various treatment conditions.

_______ represents data as a series of points connected by a line. Most appropriate when IV is continuous & quantitative, good to illustrate functional relationships among variables

line graph

Measure of spread

measure of variability

Pearson R (also known as Pearson product-moment correlation coefficient)

most widely used measure of association Use it when you scale your dependent measures on an interval or ratio scale (continuous scale) Provides the direction & magnitude of relationship between 2 sets of scores - -1 to +1 - + or - to describe direction of the relationship (i.e., of the scatter) - + correlation indicates a direct relationship (as the values of the scores increase in one, so do the values in the other) - -correlation indicates INVERSE relationship (as the value of one score increases, the values of the other decreases) - # describes the magnitude of the relationship (strong vs. weak) - sensitive to skewness/outliers (because of the mean), range of scores (if it varies too much), homoscedascity (have the same finite variance) curvilinear relationships

If the long tail goes off to the left, downscale is considered ___ distribution.

negative (-) skewed distribution

Many variables encountered in psychology tend to produce a distributive that follows more or less a mathematical form known as the ____.

normal distribution

Case Study

observations of an individual client, dyad, or group made under unsystematic and uncontrolled conditions, often in retrospect. the lack of experimental control makes it difficult to rule out other factors that may have contributed to the observed change.

Another name for the vertical axis is

ordinate or y-axis (dependent variable)

_____ are extreme scores that lie far from the others, well outside the overall pattern of the data.

outlier or gaps

If the long tail goes off to the right, upscale is considered ___ distribution.

positive (+) skewed distribution

What would be the advantages and disadvantages for conducting a AB design?

presents only single administration of each condition therefore lacks intrasubject replication

Multiple Baseline Designs:

provide a solution to irreversible changes in behavior resulting from treatments; these designs simultaneously sample several behaviors within the experimental context to provide multiple behavioral baselines. - most used with multiple behaviors in one subject, with each behavior targeted at different times - - 2 or more data collection baselines on different dependent measures (one of the variables serve as a control). - - Those dependent measures, however, must be independent of each other. - - Recommended to use 4 or more measures, and increase the number of baselines

Boxplots- Five-number summary

provides a useful was to boil down a distribution into just a few easily grasped #'s, several of which are resistant to the effects of skew and outliers & all are based on the ranks of the scores. 5 numbers = 1. Maximum: largest score in distribution 2. Q3 3. Median 4. Q1 5. Minimum: smallest score in distribution - SPSS cuts off outliers, defining them as 1.5 box lengths away from edge of box

Within-Subjects Designs (Within Groups; Repeated Measures)

randomly assign subjects to groups, then expose each group to different single experiment treatment -all subjects get each level of the IV

In _______ each pair of scores is represented as a point on the graph, often include a best-fitting straight line to indicate the general trend of the data points shown in the plot. Good way to show correlations.

scatter plot

In research using a correlational strategy, the data from the two dependent measures are often plotted as a _______.

scatter plot

Benefits in graphing data include

shows relationships clearly; allows to you evaluate data for appropriate statistic application

Range

simplest & least informative: distance from the lowest to the highest scores; doesn't take into account the magnitude of the scores between extremes Sensitive to outliers

A long tail trailing off in one direction and a short tail extending in the other is referred to as ____.

skewed distribution

Problems with unequal baseline (baselines of different subjects in an experiment level off at different values despite experiencing similar conditions) in single-subject designs?

sometimes not a problem if differences between A & B are equal (just add a secondary y-axis). Solution: secondary y-axis, manipulate variables for that subject (e.g., longer baseline).

If you create 1 column for participants IDs, a column for the treatment level (dummy-coded), and a column for each DV you have mostly likely used ___ method.

stacked

When organizing your data, you should mostly likely used _____ method.

stacked

John Tukey is know for creating what graph?

stem plot aka stem-and-leaf-plot

___ is considered a quick alternative to the histogram?

stemplot aka stem-and-leaf-plot

Error variance

the variability among scores caused by variables other than your IV. Extraneous variables such as age, gender, &personality

Fisher et al.'s (2003) CDC method entails Conservative Dual-Criterion Method for Single-Case Research

these four steps: 1. Count the number of data points in the treatment phase. 2. Look that number up in Table 1 to determine the number of points in the predicted direction of the treatment effect (i.e., either improvement or reduction in the outcome measure) needed to conclude that systematic change occurred. 3. Count the number of points in the treatment phase that are above both lines (or below both lines if the treatment is attempting to reduce the outcome measure). 4. If the number of data points from Step 3 is greater than or equal to the number required by Table 1 in Step 2, conclude that systematic change occurred from baseline to treatment. If not, conclude that there is not sufficient evidence of systematic change.

Quasi Experimental Designs

those that resemble experimental designs but use quasi-independent rather than true independent variables:

When organizing your data if you have each subject's data recordings are listed and paired with subjects number you have mostly used ____ method .

unstacked

stem-and-leaf plot

used to simplify displaying distributions Stem: enter the first digit from both sides of the range, then enter the middle unit first digits. Leaf: Once you have the stems (e.g., the tens place), enter the rest of the digit ends in order in the right column. Ex: 42, 43, 51, 56, 56, 58, 63, 64, 65, 66, 66, 67, 69, 71, 71, 71, 72, 74, 74, 92, 108 4 23 5 1668 6 3456679 7 111244 8 9 2 10 8