BPK 304
When is an Independent t-test used?
- Comparing 2 means - Total sample size less than or equal to 120 - Means from 2 independent groups
What statistical tests allow researchers to determine a difference? Relationship?
- Is there a difference? (T-tests, ANOVA, ANCOVA, and their non-parametric equivalents) - Is there a relationship? (Correlation, regression, and their non-parametric equivalents)
When is a Paired T-test used?
- comparing 2 means - Total sample size less than or equal to 120 - means from 1 group (i.e. paired)
When is a one-way RM ANOVA used?
- comparing 2 means - total sample size greater than 120 - means from 1 group (i.e. paired) If only between-groups factors: RG ANOVA If only within-groups factors: RM ANOVA If between-groups & within-groups factors: Mixed
When is a one-way RG anova used?
- comparing 2 means - total sample size greater than 120 - means from 2 independent groups If only between-groups factors: RG ANOVA If only within-groups factors: RM ANOVA If between-groups & within-groups factors: Mixed
What are normal probability plots?
Correlation between observed and expected cumulative probability is a measure of the deviation from normality. - looking to see line of identity. (green line) Left - data normal cause points fall on line of identity.. If not falling line of identity it is skewed. Should always look at data. 3 easy ways to determine if skewed or normal - frequency pltots, CFD, normal probablity plots.
You wish to test push and pull forces on a laundry cart using 4 different types of castors in a group of 35 hospital employees. What are the DVs? IVs? # of levels of the IVs? What type of analysis would you use?
DV: 2- push and pull forces IV: 4 types castors Levels: 4 Means: 4 for push, 4 for pull - Don't combine DV's, each are treated separately with ANOVA - RM ANOVA - One way ANOVA (same for push and pull) - If find significant effect of castor type? Do post hoc to find which means different from another
What is signal averaging?
• (a) (b) and (c) are QRS peak aligned ECG signal epochs • (d) is the result of averaging 100 such epochs • This works because noise tends to be random and cancel out, while true signal has a consistent pattern - Divide long signal up into fixed amounts of tie (epoch), know that epoch long enough for signal of interest to occur within. Then cut signal into epoch's (done with code). Take each epoch and line up in time (time=0). Then at each point in time take average value of the signal (get rid of underlying noise because randomly distributed). Need to line up signals (ex. QRS in ECG)
How can Smoothing Serial Data by Fitting Mathematical Equations be achieved?
Equations are often used to smooth noisy data • You can find an equation to fit most data • Can also be used for imputing (estimating) missing values - Ex. line, curvilinear. By fitting equation to data points will give trendline (smooth representation) and ability to interpret data points which are missing.
What are the Critical values of t, independent t-test?
H0: there is no difference between means H1: there is a difference between means Degrees of freedom (df) - Equal sample sizes: 2n-2 - Unequal sample sizes: n1 + n2 - 2 If tcalc > tcrit, then significant difference - critical value goes down as degrees of freedom goes up. If get test statistic greater than 2 will generally be significant. (independent t-test)
What is a cumulative frequency distribution?
median - data point where 50% data points fall at or below. CFD - with different curve indicates not normal distribution
What are weighted moving averages?
Centralpointsaregivenmoreimportance • Arbitraryweightingscheme - e.g.,13531 • Tends to result is less attenuation of amplitude than unweighted moving averages - Giving more weight/importance to different points averaging. Every point averaging has same amount of importance. Can apply weighting scheme. Most weight/importance to middle point and less weight to points further away to will tend to results in less change in amplitude. Need to figure out which weighting scheme appropriate for data you have.
What is serial data?
- Repeat observations overtime on individual participants. Ex height and weight on infants. • Serial data are collected over time ("longitudinal"). • Examples: - height and weight measured monthly in infants - post-intervention measurements at multiple times - digitized analog signals • Data points are not independent. • Serial data are often noisy (not smooth). • Therefore, we often need to smooth serial data to remove noise and uncover the underlying signal. - Data points no longer independent of each other. Trends are apparent. Data somewhat noisy and deviated from smooth pattern. Smooth data - make it look less noisy
Which tests are used when comparing more than 2 means?
1 factor (A) - one-way ANOVA - Main effect: A 2 factors (A,B) - Two-way ANOVA - Main effects: A,B - Interactions: AxB 3 factors (A,B,C) - three-way ANOVA - Main effects A,B,C - Interactions: AxB, AxC, BxC, AxBxC If only between-groups factors: RG ANOVA If only within-groups factors: RM ANOVA If between-groups & within-groups factors: Mixed - Take levels of each factor and multiply to determine number of means. Simple scenario - comparing 2 means. Where do means come from? More than 2 means - no t-tests only ANOVAS. How many factors? Not going to deal with 3-way ANOVAS and 2 factors. - Abbreviations: RG, randomized groups; RM, repeated measures
What are the steps to testing for statistical significance?
1. Collect data from a sample 2. Calculate appropriate test statistic (e.g., t statistic, F statistic) 3. Compare test statistic to its critical value. Critical value depends on sample size and predetermined significance level, α. Critical values are found in stats texts and are incorporated into EXCEL and SPSS output. a) If test statistic > critical value (big test statistic), then p value < α. Reject null hypothesis (H0). Result is 'statistically significant.' b) If test statistic ≤ critical value (small test statistic), then p value ≥ α. Do NOT reject null hypothesis (H0). Result is not 'statistically significant.'
What are the steps to the scientific method?
1. Define the problem 2. Develop a research question and hypothesis 3. Test the hypothesis 4. Compile the results 5. Communicate the results
What are the steps in mathematical modelling?
1. Identify and understand the underlying mechanism 2. Translate that phenomenon into a mathematical equation 3. Test the fit of the model to actual experimental data -Modify the model to fit the data that we have (empirical information) 4. Modify the model according to the results of the experimental evaluation
How do we smooth serial data?
1. Moving averages (unweighted and weighted) 2. Signal averaging 3. Fitting mathematical equations Smoothing serial data: - Moving averages ○ Unweighted & weighted - Signal averaging - Fitting Mathematical equation ○ Mathematical model
What is involved in Analog to Digital (A/D) Conversion?
1. Record Analog Signal - Transducers • transforms one form of energy to another form • E.g., pizoelectric crystals and load cells turn force into voltage - Electrodes • sense biological signals that are natural voltages • E.g., EEG, ECG, and EMG electrodes 2. Analog Signal Conditioning - electronic circuitry to modify the signal before it enters the computer for digitization. - Amplification - Filtering - Integration 3. Convert analog signal to digital with an A/D conversion board + software - Necessary to digitize the analog signal - A/D conversion board samples the analog signal at a set frequency - Stores it as binary information - Operations of the A/D board are controlled by software
What are the Functions of A/D Board?
1. Sampling - Analog signal is sampled at a set frequency - Nyquist rule: sample at least twice the highest frequency (Hz) of the signal to avoid aliasing 2. Quantitization: Number of levels of voltage is determined by the number of bits in conversion. The number of bits used to represent each conversion affects how many possible different values can be resolved from the converter. 3. Encoding: Assigning a digital code
What are the Ideal Characteristics of a Mathematical Model?
1. Simple 2. Fits the experimental data well 3. Has biologically meaningful parameters
/What is a t-test, ANOVA, and ANCOVA?
1. t-test - Compare 2 means from relatively small samples - Independent t-tests and paired t-tests 2. ANOVA - Analysis of Variance - Compare ≥ 2 means - One-way, Two-way, Three-way - Randomized groups, Repeated measures 3. ANCOVA - Analysis of Covariance - Compare ≥ 2 means and control for covariates (next week)
Who do you test between different means?
1. t-test - Compare 2 means from relatively small samples - Independent t-tests and paired t-tests 2. ANOVA - Analysis of Variance - Compare ≥ 2 means - One-way, Two-way, Three-way - Randomized groups, Repeated measures 3. ANCOVA - Analysis of Covariance - Compare ≥ 2 means and control for covariates
What are the components of a peer reviewed journal article?
Abstract - A brief, structured summary of the study Introduction - Relevant background and study objectives/hypotheses Methods - Study population, experimental protocol, statistical analysis. Should be detailed enough for another scientist to repeat the study. Results (includes tables and figures) - Clear description of results without any interpretation Discussion - Interpret results in the context of the hypothesis and existing literature - Comment on future research directions & limitations Submission Format - "Information for Authors" provided by individual journals - Attention to detail is mandatory
What is an ANCOVA?
Analysis of Covariance (ANCOVA) - Potential confounders. Influenced DV and associated with groups IV. Adjusting for these variables in ANCOVA • When you compare groups of individuals, there may be important differences between the groups that influence the dependent variable. • Fortunately, when you test for a difference between means, you can take into account (or "adjust") for a relationship between the dependent variable and another continuous variable (covariate) with ANCOVA. - Ex. Something biologically difference about male and female muscle. Could control for girths, to test differences in strength, but men tend to have larger. Option 2: measure forearm size and control for statistically
What is a coefficient of variance? What is a f-statistic?
Coefficient of variance = SD/mean. F statistic- test statistic from ANOVA. F ratio decreases with overlap
When, why, and how is ANOVA used?
Analysis of Variance - ANOVA When is ANOVA used? - Used to test for differences among multiple (>2) group means - Also used to test for differences between 2 means when sample size is large (total n > 120) Why is ANOVA used? - It's useful because multiple t-tests result in increased chance of type 1 error How is ANOVA used? - F (ratio) statistic is calculated and is evaluated in comparison to the critical value of the F (ratio) statistic
What does inferential statistics allow us to do?
As the name suggests, Inferential Statistics allow us to make inferences (conclusions) about a population, based upon a sample, with a specified degree of confidence. • Example: Assume that mean birth weight of babies born to mothers who receive prenatal care is 7.2 lbs. In contrast, assume that mean birth weight of babies born to mothers who do not receive any prenatal care is 5.8 lbs. • Is this difference of 1.4 lbs important? - Stats cant help us answer this. Doesnt determine importance compared to clinical. • Is this difference of 1.4 lbs due to chance? - Statistics helps us understand this. Whether results are due to chance or real phenomenon. If due to chance, probably wouldnt get same results, if not due to chance should get similar results
You wish to test push forces on a laundry cart using 4 different types of castors in 35 hospital employees and 35 hotel employees. What are the DVs? IVs? # of levels of the IVs? What type of analysis would you use?
DV: push force IV: castors (4 levels), type of employee (2levels) - 8 mean values - Castor type (within), Employee type (between groups) - Mixed ANOVA 2 way (2 factors - employee type, castor) - Castor is a repeated measures factor; Job type is between-groups factor. - If significant employee by castor interaction, interpret interaction and ignore main effects. Look for qualitatively, looking trend among different groups (ex. Hotel vs. hospital) looking for contrast. Draw some kind of contrast ex. Increased in hotel but decreased in hospital. (look at graph results and look at trendlines).
What is the SEM?
Distribution of multiple sample means. Standard deviation of sample means is called the standard error of the mean (SEM). - gives us sense of how confident we can be that mean we are reporting is true representation SEM = SD/n^(1/2) - • • Standard Error of the Mean (SEM) The SEM describes how confident you are that the mean of the sample is the mean of the population How does the SEM change as the size of your sample increases? - decrease - less error in measurement. More confidence.
What are key components to designing a study?
Ethics approval for human subjects research - University Research Ethics Board, including study protocol - Participants provide informed consent Sampling (recruiting study participants) - Specify your recruitment methods - Only random if you employ a truly random sampling method - Sample size may be determined by "power calculation" Measurement tools should be valid and reliable - Valid (accurate) tools minimize systematic measurement error. Calibration improves accuracy. - Reliable (reproducible) tools minimize random measurement error. Objective tools usually more reliable than subjective. Systematic - could be due to faulty equipment, the error may be the same for everyone but not the true value Random - natural form, expect a bit in all measurements. Need reliable and reproducible tool. No measurement tool is perfect - reliable but not valid more common than valid but not reliable Data collection instruments - what instruments will I use. force plat, BP cuff.
Explain the examination of residuals in mathematical modelling.
Examination of Residuals Residual = Actual Y - Predicted Y Ideally there is no pattern to the residuals, which means the residuals would be randomly distributed about a mean of zero. In the example on the left, however, there is a clear pattern (U-shape) indicating the lack of fit of the model. - If plot residuals, hoping residuals will be equally and randomly distributed about zero. Small values of X residuals very large. Indication that model doesn't fit data very well.
What is a F(ratio) statistic?
Figure depicts scores from 4 groups. • Red arrows illustrate variability within each group. • Black arrows illustrate variability between groups (i.e., how much each group mean varies from the overall grand mean) • The F (ratio) statistic compares these two sources of variability in the scores. • The variability between the group means, called Between Group Variability, is compared with the variability among individual scores within each of the groups, called Within Group Variability. • F (ratio) statistic increases as the between group variability increases and the within group variability decreases. - each group lies a distance away from grand mean, (represented by black arrow) between group variability - represents variability between groups. total,
What are RG 2way and 3way ANOVAS?
For 2-way ANOVA, there will be: - Two factors (main effects) considered simultaneously :A&B - One 2-way interaction (AxB) • For 3-way ANOVA, there will be: - Three factors (main effects) considered simultaneously: A, B, & C - Three 2-way interactions (AxB, AxC, BxC) - One 3-way interaction (AxBxC) • If p>0.05 for each interaction, then interpret main effects • If p<0.05 for an interaction, then interpret the interaction and not the main effects • Typically ANOVA is used only for 3 or fewer factors - regression modeling used for more than 3
What is the hypothesis?
Hypothesis: statement explaining a phenomenon under consideration, based upon researcher's understanding before any experimental testing has occurred. - preliminary answer to that research question Ex. aerobic exercise twice weekly for 30 minutes reduces perceived global fatigue levels in older adults compared to health education control.
What is the central limit theorem?
If a sufficiently large number of random samples of the same size were drawn from an infinitely large population, and the mean was computed for each sample, the distribution formed by these averages would be normal.
What are repeated measures ANOVAs?
In a repeated measures design, the same dependent variable is measured several times under different experimental conditions for each participant. • Pre- and post-test scores are the simplest RM design example - use paired t-test if there are just 2 means & sample size is small. - with 3 or more means or a large sample size, you have to use RM ANOVA. • RM designs have advantages over RG designs: - eliminate variability due to differences between subjects, which makes it easier to identify the effect of the independent variable. - often require fewer participant and less time
What are the internal and external norms for calculating z-scores?
Internal Norm A sample of subjects is measured. Z-scores are calculated based upon the mean and SD of the sample. Thus, Z-scores using an internal norm tell you how good each individual is compared to the group they come from. Mean = 0, SD = 1 - Internal Norm - how you did compared to the group. External Norm A sample of subjects are measured. Z-scores are calculated based upon mean and SD of an external normative sample (national, sport- specific etc.). Thus, Z-scores using an external norm tell you how good each individual is compared to the external group. Mean = ?, SD = ? (depends upon the external norm) - ex. compared to Kin students nationally. Athletes comparing to national norms. Mean and SD could be any value.
What is important when Reporting Statistics in Journal Articles?
It is best to report precise p values. For example: BMI was higher among upper division compared to lower division students (p=0.03). • Report p values to 2 or 3 decimals. • Avoid the temptation to state that results were almost significant, for example if p=0.06.
What are labVIEW programs?
LabVIEW Programs Are Called Virtual Instruments (VIs) LabVIEW programs are known as VIs because they imitate real instruments as Virtual Instruments 1. Front Panel • Inputs = Controls • Outputs = Indicators 2. Block Diagram • Accompanying "program" for front panel
What is labVIEW?
LabVIEW is an object-oriented programming language that is used for A/D conversion • Users operate LabVIEW via a GUI - Graphical User Interface • In a LabVIEW program you include objects, which might be a button, an input form, an image of a toggle switch, etc. • The code for objects is prewritten, and statements can be attached to the objects
What is mean, median, mode?
Mean: "centre of gravity" of a distribution; the "weight" of the values above the mean exactly balance the "weight" of the values below it. Arithmetic average. Median (50th %tile): the value that divides the distribution into the lower and upper 50% of the values Mode: the value that occurs most frequently in the distribution
What are some descriptive statistics?
Measures of Central Tendency - Mean, Median, Mode Measures of Variability (Precision) - Variance, Standard Deviation, Interquartile Range Standardized scores - comparisons to a reference distribution Percentiles
What is smoothing data with a moving average?
Moving average - raw data with local fluctuations. Average produces smoother repseatnation of signla and takes average of 3 data points. Average value pltted in middle of three data points. Move average 1 point at a time. Will create new curve, less noisy with less peaks and valleys. Shrinking the data set. 2 less in blue then red trace. Lose some data but well worth smoother representation - When add noise, amplitude increases. - Distorted in terms of amplitude, really compressed. Too much points in moving average. Always odd number because natural middle to it to plot data. Trying to enhance look of signal without distorting it.
What is the difference between a null and alternate hypothesis?
Null Hypothesis Ho - no difference between means Alternate Hypothesis Ha - there is a difference between means
How can RG ANOVA be used for multiple factors?
Test of differences between means with two or more grouping factors, such that each factor is 'adjusted' for the effect of the other. • Used to evaluate significance of individual factors (main effects) and interactions between the factors.
What is the odds ratio?
Odds ratio = 1 -> no effect of the IV on the DV (outcome) 95% Confidence interval....
Explain a Visual Test of Significant Difference between Means.
Overlapping standard error bars; therefore, no significant difference between means of A and B No overlap of standard error bars; therefore, a significant difference between means of A and B at about 95% confidence
What does a percentile score mean?
Percentile: The percentage of the population that lies at or below that score
What is the preece baines model?
Preece-Baines Model I Developed in 1978 to explain the complex curve of human growth • ht is height at time t • h1 is final height (anticipated adult height) • s0 and s1 are rate constants • q is a time constant (an age, near the age of peak height velocity) and • hq isheightatt=q
What components should the research question contain?
Research question: precise question the study will address Key components to strong research: PICO - population - intervention - what you are using to test (ex. exercise) - Comparator - Outcome - what outcome will you measure Poor example: Does exercise impact fatigue levels? Better ex: Does aerobic exercise twice weekly for 30 minutes impact (decrease) perceived global fatigue levels in older adults compared to a health education control?
How do researchers communicate the results of their studies?
Researchers have a responsibility to communicate their findings to the rest of the scientific community and to other stakeholders who fund the research (e.g., the public) and who can apply the findings (e.g., decision makers). Conferences and research symposia - Up-to-date results that are not yet published Peer-reviewed journal articles - Most highly regarded form of scientific communication Books - Often not peer reviewed, so not as highly regarded Non-traditional formats with greater reach - Blogs, social media channels, press releases, op-eds - research grants from national funding agencies. Budgets from tax payer money.
Explain the calculation of a resolution board?
Resolution is expressed in volts (or millivolts) per bit A/D voltage range of -10V to +10V = 20V 12 bit A/D board 12 bits = 2^12 = 4096 possible values Resolution = 20v / 4096 = 0.00488 V per bit (4.88 mV per bit)
What are the sources of variability?
SS = sum of squares Individual participants are indexed by i (ranging from 1 to nj) Groups of participants are indexed by j (ranging from 1 to p). If there were 2 groups and each group had 10 participants, then i would range from 1 to 10, and j would range from 1 to 2. - if add SSbetw and SSw/in get total. How different each individual from total mean. reflection of how much diff - total, between, within
What steps should be taken tp test a hypothesis? What are 2 possible outcomes?
Steps: Hypothesis, prediction, experiment, evaluate accuracy of predictions. The modify hypothesis if needs change 1) Model - A model is a hypothesis that has been shown repeatedly to hold true under certain conditions (e.g., muscle models describe force-velocity relationship) 2) Theory/Law - When a hypothesis has been tested and shown to hold under many experimental conditions it may be called a theory or law (e.g., laws of motion). Theories and laws are difficult to dismiss as they are based on repeated & consistent experimental evidence.
What are the characteristics of a normal frequency distribution?
Symmetrical about the middle. Equal amount data on both sides. Middle - mean, median, mode. Defined amount data within boundaries. 95% data within 2 SD. most data centralized. T-test rely on normal distribution
What are T-scores?
T-score - same as a z-score. Mean and SD come from external population. - standardized score a T-score, it is really just a Z-score where the reference mean and standard deviation come from an external population - (i.e., young normal adults of a given sex and ethnicity). Osteoporosis T-scores are used to classify a patient's BMD into one of three categories: - T-scores of 3 -1.0 indicate normal bone density - T-scores between -1.0 and -2.5 indicate low bone mass ("osteopenia") - T-scores less than or equal to 2.5 indicate osteoporosis • Decisions to treat patients with osteoporosis medication are based, in part, on T-scores.
What does a chi-square test do?
The chi-square tests for a difference in the proportion of observed frequencies across a given set of categories in comparison to the proportion of expected frequencies
What is the p value?
The p value associated with a statistical test is the probability of obtaining, by chance, a test statistic at least as extreme as the one that was actually observed, assuming the null hypothesis is true. - If a p value is small (e.g., <0.05), there is little chance (less than 5%) that the result you observed was due to chance. In other words, it is highly likely that the result is "real." • Before data analysis, researchers must choose a significance level, α, below which to accept a result as statistically significant. • If p < α, reject the null hypothesis H0 and conclude there is a 'statistically significant' result. • Very frequently, α is set to 0.05. Thus, p < 0.05 indicates statistical significance. - An α of 0.05 means that you would expect to find a result of this magnitude by chance 5 in 100 times. In other words, you have 95% confidence in the result. - A more stringent criteria would be α of 0.01 (99%confidence in the result). - Starting assumption is Null hypothesis is true, trying to find evidence that its not true. Small p value means small chance that observed results is due to chance. Highly unlikely result is not real. Need specify significance level. Alpha usually 0.05. - can be statistically significant without being clinically significant
What are the assumptions of an RG ANOVA?
The populations from which the samples were obtained are approximately normally distributed. • The samples are independent. • The population value for the standard deviation between individuals is the same in each group. - If standard deviations are unequal, transformation of values may be needed before running a RG ANOVA. - assuming groups are independent of one another and are approximately normally distributed, and the SD are thre same. Similar amounts of variability
Why is an independent t statistic calculated?
The t statistic is then calculated as the ratio of the difference between sample means to the standard error of the difference.
What is the difference between parametric and non-parametric statistical tests?
These parametric statistical tests require the dependent variable to be continuous and approximately normally distributed. • But what if your data do not meet these criteria? • Nonparametric statistical tests do not require the data to belong to any particular distribution. Therefore, nonparametric tests are appropriate if data are not continuous or normally distributed.
How do accelerometers work?
Transducer or Sensor -Energy converter (e.g., movement to electronic signals) -Range, sensitivity, linearity, hysteresis, drifts Data Acquisition System -Data sampler and pre- processor (e.g., raw signals to desirable parameters) -Sampling frequency, signal conditioning, digital signal processing, size, cost - filter, rectify, sum over epoch
How do you standardize scores?
Transform data into standard scores (e.g., Z-scores) Eliminates units of measurements - Z-score - eliminates units of measurement. Units of SD (unitless). Measures SD compared to mean or average. - Standardizing does not change the distribution of the data - doesnt change the shape. Converting to z-scores doenst make normal. Natural log will make more normal. Z-score shape will look the sameX - individual
What is a two-way chi-square test?
Two categorical variables are considered simultaneously (e.g., sex and smoking status). • Two-way Chi-square test is a test of independence between the two categorical variables. • Null hypothesis: there is no difference in the frequency of observations for each variable in each cell. • If the observed and expected frequencies are similar within each variable, the chi-square test will not be significant (p≥0.05). • If the observed frequencies deviate considerably from the expected frequencies in one or more categories, the chi-square test will be significant (p<0.05).
What are type I and type II errors?
Type II error (b) - There is a true difference/effect, but you miss it - Ho is False (yes difference), Accept Ho Type I error (a) - You conclude there is a significant effect/difference when there is not. - Ho is True (no difference), Reject Ho Power = 1 - b - Ho is False (yes difference), Reject Ho 1-a - Ho is True (no difference), Accept Ho Ho, null hypothesis Commonly set a to 0.05 Commonly set b to 0.20, so that power is 0.80 (if there is difference, want to be able to see it 80% of time.)
What are the types of variables involved in experiments?
Types of Variables • Independent variable (IV): the variable that you change or manipulate. - Also known as predictor variable or exposure variable • Dependent variable (DV): the variable that is observed and changes in response to the independent variable. - Also known as outcome variable or response variable • Covariates: variables that are held constant either by research design or statistical analysis. - Also known as confounders or controlled variables - IV - IV have affewhat variable do you want to change. Predictory variable. Dependent variable. - supposed to change in response o change in IV. Covariates - held constant. ex. holding age. - iV have Affect on DV. W (confounder) have affect on iV and DV.
When is a independent t-test used?
Use an independent t-test to compare means from two independent groups, e.g., compare BMI between men and women • H0: there is no difference between means • The t statistic is calculated using the difference between the means in relation to the variance in the two samples • The critical value of the t statistic is based upon sample size and the significance level, α. Critical values are found in tables at the back of a stats text and are also part of the EXCEL and SPSS output. • The calculated t statistic based upon your data must be greater than the critical value of t to accept a significant difference between means at the chosen level of significance, α - t statistic from an independent t-test quantifies the degree of overlap of the distributions
What kurtosis factor indicates a normal distribution?
Where: X = mean, Xi = X value from individual i N = sample size, s = standard deviation A perfectly Normal distribution has Kurtosis = 3 based on the above equation. However, SPSS and other statistical software packages subtract 3 from kurtosis values. Therefore, a kurtosis value of 0 from SPSS indicates a perfectly Normal distribution - only end up with positive value in numerator.
Explain the skewness coefficient.
Where: X = mean, Xi = X value from individual i, N = sample size, s = standard deviation A perfectly Normal distribution has Skewness = 0 If -1 ≤ Skewness ≤ +1, then data are considered to be Normally distributed
What do z-scores allow?
Z-scores allow measurements from tests with different units to be combined. But beware: higher Z-scores are not necessarily better performances. - allows combine info in multiple test for composite score. Z-scores are able to take average score among different measurments. - higher score i some measurements may not be desireable ex. adiposity, shuttle run. Can flip the signs to better represent the meaning of the values. - *Z-scores are reversed because lower skinfold and shuttle run scores are regarded as better performances
What is the difference between digital and analog?
l Computers use digital information (0's & 1's) l Analog signals are continuous waveforms (e.g., sound, force, pressure, light, l Analog signals can be converted to digital information (i.e., voltage that is proportional to the amplitude of the signal)
What is a 2-way ANOVA?
• A 2-way ANOVA is used when you are testing the effects of 2 independent variables (factors) on a dependent variable. • For example, what are the effects of age and sex on BMI? • With a 2-way ANOVA you can determine the main effects of each independent variable - How does age affect BMI, independent of sex? - How does sex affect BMI, independent of age? • You can also determine if there is an interaction between the two independent variables. - Does BMI change with age the same way in girls and boys? - ANOVA with 2 factors. Look at main effects and interactions.
What is the terminology for ANOVA?
• A factor is an independent variable (e.g., experimental condition) with a certain number of levels. - Sex is a factor that has 2 levels (men/women) - Exercise grouped as aerobic/resistance/flexibility is a factor with 3 levels • A between-subjects factor identifies different groups • For example, AGE (young/old) is a between-subjects factor with 2 levels. • A within-subjects factor or repeated measures factor identifies different conditions experienced by one group • For example, assume each participant completes 3 walking conditions (level/uneven/incline). Then WALK CONDITION is a within-subjects factor with 3 levels. - number of factors helps determine how many means will be calculated. 2:42, If 2 levels multiply the factors
What is the resolution of an A/D board?
• A measure of the smallest amplitude value as a percent of the full scale voltage range to which a quantity can be determined • Voltage ranges of A/D boards are commonly: -10v to +10v -1v to +1v -100mv to +100mv
What is a Mixed ANOVA?
• A mixed ANOVA is a specific type of 2-way ANOVA where one factor is a between-groups factor and one factor is a within-groups (repeated measures) factor. • For example, assume you tested gait speed over 3 different distances (short, medium, long) in young and elderly adults • You have: - one between-groups factor = age - one within-subjects factor = walk distance
What is A/D software?
• A/D conversion requires A/D board control software • LABVIEW: LABoratory Virtual Instrument Engineering Workbench
When is a paired t test used?
• Also called t-test for correlated data • Use a paired t-test to compare means from two sets of paired or dependent observations - "before and after" experiments - repeated measures experiments - bilateral symmetry (e.g., right vs. left side) - E.g., compare stress hormones in a group of subjects before and after a yoga class • H0: the mean of the differences between paired observations is not significantly different from zero. • If tcalc > tcrit, then significant difference - degree of freedom n-1 - The calculated t statistic is evaluated in a similar way as the independent test
What are the differences between skewness and kurtosis?
• Deviations in shape from the Normal distribution. • Skewness is a measure of symmetry, or more accurately, lack of symmetry. - Skewed (deviaiton) if not symmetrical. - A distribution, or data set, is symmetric if it looks the same to the left and right of the center point; it is skewed if it looks non- symmetric to the left and right of the center point. • Kurtosis is a measure of peakedness. - Reflects how peaked the distribution is. High kurtosis - high peak not much to either side. low kurtosis is flatter curve with lots to each side. - A distribution with high kurtosis has a distinct peak near the mean, declines rather rapidly, and has heavy tails. - A distribution with low kurtosis has a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case. - long tail to negative (negatively skewed) long tail to positive (positively skewed) - platykurtic - flat leptokurtic - extremely peaked. Pay attention to skewness more.
What is Mathematical Modeling of Serial Data?
• Differs from simple equation fitting in that the parameters of the equation must have biological meaning. • Mathematical models can be used to: - Smooth noisy data - Explain phenomena - Predict future results - Model parameters have meaning. Some meaning to predictors in model. Usually have causal interpretation.
What is digital information encoded in?
• Digital information is encoded in BITs = BINARY DIGITs - either1or0,highorlow,yesorno • Computers operate with binary not decimal numbers - Decimal system = Base of 10 - Binary system = Base of 2 • Computers therefore require all numbers to be represented in the binary system.
What is the difference between randomized group vs. repeated measures ANOVA?
• If we are dealing with only between-subjects factors, we use Randomized Groups (RG) ANOVA. - Similar to the independent t-test. • If we are dealing with only within-subjects factors, we use Repeated Measures (RM) ANOVA. - Similar to the paired t-test. • If we are dealing with both between-subjects factors and within- subjects factors, we use Mixed ANOVA.
What is a "Post Hoc" Test?
• If you find a significant main effect from an ANOVA for a factor that has 3 or more levels, you do not know initially which means are different from one another. - Figure out which means are different from one another. Done after significant main effect or interaction • You can use a post hoc test to determine which means are different from one another. • Similarly, if you find a significant interaction from an ANOVA, you can use a post hoc test to determine which means are different from one another. • Post hoc tests are so named because they are completed after one observes a significant main effect or interaction. • If you are having trouble understanding a concept, please come see me for help.
What are the different types of non-parametric tests?
• Is There a Difference? - Wilcoxson signed rank test: Analogous to paired t-test. - Wilcoxson rank sum test: Analogous to independent t-test. - Chi-square: Analogous to ANOVA. It tests differences in the frequency of observations of categorical data. • Is there a Relationship? - Rank Order Correlation: Analogous to the Pearson correlation coefficient . These tests examine relationships between ordinal variables. Includes the Spearman's Rank Order Correlation (rs) & Kendall's Tau (τ). • Can we predict? - Logistic Regression: Analogous to linear regression. It assesses the ability of independent (predictor) variables to predict a dichotomous outcome variable.
How do you Examine the Fit of the Model?
• Least Sum of Squares • Shape of the curve vs. shape of the model - Can visual inspect plot of data and plot of model to determine overlap. Ex. line doesn't fit data, linear model not appropriate when shape of curve doesn't match shape of model)
What is maximum likelihood with logistic regression?
• Linear regression - least sum of squares • Logistic regression is nonlinear. For logistic curve fitting and other nonlinear curves the method used is called maximum likelihood - Values for the coefficients (e.g., B0 and B1) are picked randomly and then the likelihood of the data given those values of the parameters is calculated. - Each one of these changes is called an iteration - The process continues iteration after iteration until the largest possible value or Maximum Likelihood has been found. - The loss function quantifies the goodness of fit of the equation to the data.
What is logistics regression?
• Logistic regression is analogous to linear regression analysis in that you produce an equation to predict a dependent variable from independent variables • Linear regression used continuous dependent variables. • Logistic regression uses categorical dependent variables. - Most common to use binary dependent variables. • Binary variables have two possible values - Yes or No answer to a question on a questionnaire - Had an event vs. did not have an event (e.g., cancer diagnosis) • It is usual to code binary variables as 0 or 1 (e.g., no=0, yes=1) In logistic regression, the dependent variable is a logit or log odds, which is defined as the natural log of the odds: In logistic regression, the estimated parameter is an Odds Ratio.
What are the differences between one- and two- tailed tests?
• Most tests of significance are two-tailed. - Allot half of alpha to testing for a significant difference in one direction and the other half of alpha to testing for a difference in the other direction. - the null hypothesis can be rejected regardless of the direction of the difference or relationship. • One-tailed tests of significance are used when the researcher is sure that differences or relationships can occur only in one direction. - You allot all of alpha to testing for a significant difference in one direction.
What does it mean to define the problem?
• Observe a phenomenon and gain a deep knowledge of it • Conduct a literature review by thoroughly searching and reviewing the relevant research literature
What is a One-way ANOVA?
• One factor (hence, one-way) - HO: There is no difference in means - HA: At least one mean is different • Factors can have 2 or more levels - Sex: male, female (2 levels) - Physical activity: low, moderate, or high (3 levels)
What is the variance and standard error?
• The variance of the difference between means is the sum of the two variances. • The standard error (S.E.) of the difference between means is then estimated by adding the variances (squares of the standard deviations), dividing by the sample size, and taking the square root.
What is a 3 way ANOVA?
• Three factors considered simultaneously, e.g., 2 Group (glaucoma, control) x 3 Lighting (normal, dim, sudden change) x 2 Motion (stationary, in motion). • Three main effects: Group, Lighting, Motion • Three 2-way interactions: Group x Lighting, Group x Motion, Lighting x Motion • One 3-way interaction: Group x Lighting x Motion
What is a type I and II error rate?
• Type I error rate (Alpha, α): - The probability of rejecting H0 when it is true. (i.e., mistakenly concluding there is a difference when there is not) (Bad error) - If you select alpha=0.01 instead of alpha=0.05, you reduce the probability of making a Type I error. But, you increase the sample size requirements of your study and you may increase the probability of a Type II error. • Type II error rate (Beta, b): - The probability of NOT rejecting H0 when it is false. (i.e., "missing" a true difference). (Not as bad an error)
What are used to measure variability?
• Variance - whats the spread in the data. How far are points away from the centre • Standard Deviation (SD) = Variance^1/2 • Range is approximately = +or-3 SDs (minimum to maximum) For Normal distributions, report the mean and SD For non-Normal distributions, report the median (50th %tile) and interquartile range (IQR, 25th and 75th %tiles)
What is Post Hoc testing?
• What? Post hoc simply means that the test is a follow-up test done after the original ANOVA is found to be significant. • Why? If you are comparing 3+ means and find a significant difference with ANOVA, post hoc tests allow you to determine which means are different. • How? You can do a series of comparisons, one for each two-way comparison of interest. • E.g. Bonferroni, Scheffe, or Tukey's post hoc tests. • The Bonferroni and Scheffe tests are conservative and therefore are reasonable choices. - post ANOVA - done to figure out where difference in means and why
When do you use mean, median, mode?
• When do you use mean, median, or mode? - Height - mean - Skinfolds - median - House prices in Vancouver - median - Vertical jump height - maximum - not central tendency - things that are normally skewed we report mean, if not normal report median. Because Mean can be affected by outliers. - objective tests have less random error, subjective tend to have more random error. Dealing with less background noise - some situations not feasible to get multiple measurements (ex. max exertion test, blind experiment)
Which software is used to gather results?
• With EXCEL and SPSS it is easy to do data analysis • But, make sure you do the correct analysis • Attentiontodetailisimportant - E.g., in SPSS, use the correct Split File or Select Cases
What is the spearmen's rank order correlation?
• You want to evaluate the relationship between variables, where neither of the variables is normally distributed. • The calculation of the Pearson correlation coefficient (r) is not appropriate in this situation (if one of the variables is normally distributed you can still use r). • If both are not normally distributed then you can use: - Spearman's Rank Order Correlation Coefficient (rs) - Kendall's tau (τ). - These tests rely on the two variables being rankings.
What are the differences in linear vs. logistic regression models?
•Linear vs. Logistic Regression Models General form of a linear regression model: Y=B1X1 +B2X2+B3X3......+Bo Y is a continuous, normally distributed variable, e.g., blood pressure in mmHg. General form of a logistic regression model: Logodds(Y)=B1X1 +B2X2+B3X3......+Bo Y is a binary variable, e.g., heart attack (yes/no) • • • • You can predict probabilities from a logistic regression model P is the probability of a 1 (the proportion of 1s, the mean of Y) e is the base of the natural logarithm (about 2.718) B0 and B1 are coefficients from the logistic model. Recall, probabilities range from 0 to 1.
