Research Design and Statistics Exam 7

descriptive statistics

Summarize the characteristics of a sample.

Examples of descriptive statistics

measures of central tendency
measures of variation/dispersion
Shape/type of distribution

inferential statistics

Test for significant differences between groups and/or significant relationships among variables

Examples of inferential statistics

t-ratio
F-ratio
Chi-square
etc...

dependent variable

The outcome factor; the variable that may change in response to manipulations of the independent variable.

independent variable

The experimental factor that is manipulated; the variable whose effect is being studied.

interval variable

a variable used for observations that have numbers as their values; the distance (or interval) between pairs of consecutive numbers is assumed to be equal. Zero has no meaning

ratio variable

a variable that meets the criteria for an interval variable but also has a meaningful zero point

mean

the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores. Influenced by outliers

Mode

the most frequently occurring score(s) in a distribution.

Only measure of central tendency that can be analyzed with qualitative/categorical data

bimodal distribution

A distribution (of opinions) that shows two responses being chosen about as frequently as each other.

Sample distribution

Just the distribution of the data from the sample

sampling distribution

the distribution of values taken by the statistic in all possible samples of the same size from the same population

Histogram

a bar graph depicting a frequency distribution.

absolute frequency

the number of times a score or value occurs in a data set

relative frequency

the fraction or percent of the time that an event occurs in an experiment

normal distribution

A function that represents the distribution of variables as a symmetrical bell-shaped graph.

skewed distribution

a representation of scores that lack symmetry around their average value

positively skewed

a distribution that trails off to the right

negatively skewed

a distribution that trails off to the left

Leptokurtic

normal curves that are tall and thin, with only a few scores in the middle of the distribution having a high frequency

Platykurtic

flat curve

standard deviation

a computed measure of how much scores vary around the mean score. Inflated by outliers

Standard deviation and distribution

1 SD = 68%
2 SD = 95%
3 SD = 99%

coefficient of variation

A measure of relative variability computed by dividing the standard deviation by the mean and multiplying by 100. Measures variation compared to the size of the mean

standard error of the mean

estimate variability of population, degree of error associated with repeated samples. Estimates precision of the sample mean

interquartile range

The difference between the upper and lower quartiles.

confidence interval

the range of values within which a population parameter is estimated to lie. Measure of precision

z-score

a measure of how many standard deviations you are away from the norm (average or mean)

level of confidence

probability that you're right, estimation that the population mean is correct

probability error

probability that you're wrong, level of chance occurs

two-tailed test

A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution.

Simply checking for differences (exercise protocol in land or water produce more strength gains)

one-tailed test

a hypothesis test in which the research hypothesis is directional, positing either a mean decrease or a mean increase in the dependent variable, but not both, as a result of the independent variable. (will an exercise protocol on land produce greater strength gains)

null hypothesis

a statement or idea that can be falsified, or proved wrong

alternative hypothesis

The hypothesis that states there is a difference between two or more sets of data.

Steps in Hypothesis Testing

-state null and alternative hypotheses
-Determine level of significance
-Compute test statistic
-Make a decision
-Relate statistical hypothesis back to research hypotheses

p-value

The probability level which forms basis for deciding if results are statistically significant (not due to chance).

alpha value

level at which significance is decided. Typically .05. Avoid type I error

Type 1 error (alpha)

Rejecting null hypothesis when it is true (false positive)

Type II error (beta)

acceptance of the null hypothesis when the null hypothesis is false (false negative)

statistical power

the likelihood of finding a statistically significant difference when a true difference exists. 1-type II error. Probability of avoiding a type II error

hypothesis testing limitations

-never know the truth
-skirts around the issue
-bound by tradition

range

the difference between the highest and lowest scores in a distribution

Variance

a measure of the spread of the recorded values on a variable. Larger variance=further from the mean and vice versa

Median

the middle score in a distribution; half the scores are above it and half are below it. Is not impacted by outliers

effect size

a measure of the strength of the relationship between two variables or the extent of an experimental effect. Represents the number of SD's by which the score changes from baseline to post-treatment

beta level

probability of making a type II error

How power can be used

-A priori
-Post hoc

Factors affecting statistical power

-Mean differences (greater discrepancy=more powerful)
-Sample size (Larger sample=smaller SEM=more power)
-1 vs 2 tailed-tests (One tailed=more powerful due to altered critical value)

sample size estimation

Estimate the size of sample necessary to accomplish the purposes of the study
-Alpha level
-Desired power
-Effect size

When lower sample size can be used

-Anticipate finding a large discrepancy
-Less variability in the measurement
-Greater risk of type II error
-Alpha is set at 0.05 rather than 0.01
-A one-tailed test is appropriate

Inference

decisions based on probability

Tools to evaluate the effect of an intervention

-Statistical differences
-Effect size
-Minimally clinically important difference
-Dichotomous outcomes

Minimally Clinically Important Difference (MCID)

The smallest difference in a measured variable that signifies an important rather than trivial difference in the patient's condition. The smallest difference a patient or clinician would perceive as beneficial, and that would result in a change in the management of the patient.

standard error of measurement

Variation in scores due to unreliability of the scale/measure used. Precision error

Minimal Detectable Change (MDC)

the amount of change that just exceeds the standard error of measurement of an instrument. Minimal amount change that isn't likely due to chance variation

Determines MCID

-Expert consensus (doesn't involved patients)
-Anchor based (could cause bias but includes the patients)

dichotomous outcome

when only two options are available to a question, such as "yes" or "no". Responders/showed improvement vs non-responders/showed no improvement

Absolute Benefit Increase (ABI)

the absolute value of the difference in rates of positive outcomes between the intervention group and the control group (expressed as a percentage)

Relative Benefit Increase (RBI)

the absolute value of the rate of increase in positive outcomes for the intervention group relative to the control group (expressed as a percentage)

Number needed to treat

represents the number of patients who must be treated in order to prevent one adverse event. 1/ABI. Smaller NNT in short time frame can be interpreted as a great benefit

Scatter plot

A graph with points plotted to show a possible relationship between two sets of data.

Venn Diagram

Diagram used to communicate a relationship between three variables

line graph

Communicates a comparison, displays a pattern or trend over time. Used only if both variables are numbers

bar chart

Used when only the dependent variable is numerical. Shows a comparison

pie chart

a chart that shows the relationship of a part to a whole

stacked bar chart

A bar chart in which each bar is broken into rectangular segments of a different color showing the relative frequency of each class in a manner similar to a pie chart.

Graphs for distribution

One variable=bar graph or histogram
two variables=scatter chart
three variables=3D chart

Figures

No titles, legends and captions only.

Figure captions

-Brief title/heading
-Experimental details
-Definitions of symbols, lines, bar patterns, abbreviations
-Statistical information

Tables

Present numerical data but do not use relationships or trends. Should have a title

Scientific merit components

-Relevance
-Originality
-Importance
-Design/methodology
-Analysis/interpretation

Formal research session

-10-15 minutes
-12-18 slides (1 slide/minute)
-3-5 minute question period

Platform/podium presentations evaluation

-Scientific merit
-Presentation style
-Technical aspects

Presentation technique

-Organize content
-Explain graphics
-Stick to time allowed
-Limit note use
-Anticipate questions

Fonts

-No more than 2 used
-At least 28 pt for text and 40 for titles
-Limit bold, italics, and underline
-Avoid all caps

Technical aspects

-Six lines a slide and 6 words a line
-Phrases
-Bullets
-Consistency
-Alignment
-Graphics (don't overdo)

Poster presentations

Stimulate interaction about results

-Identify 2-3 key points
-Select relevant methods and results
-Adapt to audience
-Handouts and anticipate questions

-30 seconds=gist of poster
-10 minutes= all införmation

Poster mechanics

Left to right and up to down
-Serif fonts
-Concise
-50:50 graphics to text

Thematic poster presentation

Posters are grouped by a general theme

-More informal
-3-5 minute summary
-Audience asks questions

Parametric

inferential statistical tests involving interval- or ratio-level data to make inferences about the population. Data fits a normal distribution

non-parametric

A category of statistical tests used when certain assumptions about the data are violated (i.e., normal distribution) or when using ordinal (ranked data). Examples of non-parametric tests include the sign test, Wilcox signed rank test, and the Mann Whitney test.

Parametrical differences tests

t-test
ANOVA

Parametrical relationships tests

correlation
regression

Correlation

2 variables perform a synchronized way, or they are associated with each other

regression

a change in one variable causes a change in the other

r-value

Sign denotes the nature of the association and the value denotes the strength of the association

Positive r value

positive correlation, One variable increases the other increases and vice versa

negative r value

Inverse relationship

Limitations of correlations

-Cannot be taken to imply causation
-Does not allow us to go beyond the data that is given

spurious correlation

an apparent but false relationship between two (or more) variables that is caused by some other variable

Pearson product-moment correlation coefficient

A type of correlation coefficient used with interval and ratio scale data. In addition to providing information on the strength of relationship between two variables, it indicates the direction (positive or negative) of the relationship.

Intraclass Correlation Coefficient (ICC)

relationship among repeated measures; magnitude

internal consistency

Questionnaire relationships

Cronbach's alpha

a correlation-based statistic that measures a scale's internal reliability. If the questions within a section are correlated with each other than you can be fairly confident in the subscale information

Correlation test

If P

line of best fit

a line drawn in a scatter plot to fit most of the dots and shows the relationship between the two sets of data. Minimizes residuals

error/residual

Vertical distance from any point to the line. Compares predicted value vs actual value

standard error of estimate

Estimate variability of prediction errors when using a regression equation to predict Y from X

Linear regression assumptions

-Linear relationship
-Homoscedasticity
-Normality of the error distribution