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76 Cards in this Set
- Front
- Back
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Standards of Measurement
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- Mass (kg)
- Distance (m) |
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Data
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Results of Measurements
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Classifications of Data
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1. Non - parametric
2. Parametric Data |
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Non - Parametric Data
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- Does not meet the assumptions of normality.
1. NOMINAL SCALE (frequency data): -- Mutually exclusive (one or the other) and exhaustive (option for everyone) categories -- No qualitative differences between categories -- Number of data points in each categories is the frequency -- Ex: Sex (not gender), ethnicity 2. ORDINAL SCALE (rank order scale): -- Qualitative order to the data, however, no equal differences between data points -- Ex: tournament rankings, athletic team polls, Olympic medal |
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Parametric Data
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- meet the assumptions of "normal" data
1. INTERVAL SCALE: -- equal units, or intervals, of measure -- no absolute zero point, so negative values are possible -- Ex: temp (f or c), used to judge performances in sports. 2. RATIO SCALE: -- Based on order -- Points are equidistant and proportional (only if u dont have neg, which is rare) -- Zero is the absence of value -- Ex: time, height, weight, mass, distance |
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Statistics
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- Mathematical technique for organizing, analyzing and presenting data for evaluation.
- In order for statistics to be acceptable, data must be: 1. Reliable 2. Valid 3. Objective |
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Can something be reliable, but not valid? Visa versa?
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??
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Reliable Data
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Reproducible under similar conditions; consistency
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Valid Data
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- Appropriateness of the test in measuring what it is designed to measure
- Ex: 40 m dash measuring ATP/CP |
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Objective Data
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Data is collected without bias
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Variables
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- Characteristics of a person, place, or thing that can assume more than one value
- Ex: Height, weight, 1.5 mile run 1. Variable Comparisons 2. Constant 3. Characteristics of Variables 4. Types of Variables |
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Variable Comparisons
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- WITHIN subjects: An individual may score differently on the same variable over a period of time.
- BETWEEN subjects: Different individuals may score differently on the same variable. |
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Variable Constant
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- Characteristics that can only assume one value
- Example: meters in a kilometer (1000), meters in a mile, cm in an inch, and pounds in a kg. |
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Characteristics of Variables
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1. Continuous variable can assume any value (distance, temperature)
2. Discrete variables are limited to certain whole numbers, usually integers (number of ppl, HR) |
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Types of Variables
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1. INDEPENDENT VARIABLE (IV): free to vary; it is permitted to exert influence over other variables and is controlled by the researcher.
- It is predicted to have an effect on the dependent variable - "predictor variable" 2. DEPENDENT VARIABLE (DV):affected by the researchers manipulation of the IV and not "free" to vary; is the variable ebing measure for analysis - aka "Outcome Measure" 3. INTERVENING VARIABLE: An extraneous variable that is not controlled for by the researcher and may have an unknown effect on the DV. |
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Theory
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- Belief regarding a concept or series of related concepts
-- Not necessarily true of false -- Produces hypotheses that can be tested via experimentation (sliding filament theory) |
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Hypothesis
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- Prediction that can be tested to determine whether or not it is correct
-- More specific than a theory -- After testing; the odds that a hypothesis is correct or incorrect can be stated -- Based on ROL -- Must be stated so that is can be statistically tested (research question) |
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Theories and Hypotheses
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- A theory may be accepted as true if many hypotheses related to it are found to be true (by original and validation)
- Theories are usually revised many times over years, or even centuries - Some theories are abandoned after experimentation |
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Null Hypothesis
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(Ho)
- predicts NO difference between groups or treatments - States that any differences that are observed are due to random errors, or chance - Ho is the hypothesis tested by statistical analysis - Ho and H1 are mutually exclusive, if one is true the other is false. |
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Research Hypothesis
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(H1)
- predicts the relationships or differences btw or among groups of subjects or treatments - H1 not tested statistically |
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Probability
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- Statistical analysis report the probability that Ho is true
- Large probability: P > 0.05 that Ho is true, we accept Ho - Small probability: P < 0.05 that Ho is true, we reject Ho and accept H1. (P< 0.05 means that there is a less tan 5% chance that Ho is true) |
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Validity Issues
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1. Internal Validity
2. External Validity |
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Internal Validity
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- Control within an experiment to determine that the results are due to the I.V. applied (i.e. Design of the study)
- A control group can be used to monitor if a "learning effect" occurs - A familiarization trial - Intervening variables: should be minimized - Instrument error: failure of equipment to provide accurate data. Regular calibration is essential. Investigation Error failure of the investigator to accurately record data. |
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External Validity
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- The ability to generalize the results of a study to the population from which the sample was drawn.
- Needs to be random, if not is does no represent the population |
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Statistical Inference
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- The process of generalizing from a sample to a population.
- External Validity 1. Subjects are assumed to represent the pop., so it can estimate the characteristics of the population 2. Error in predicting from a sample is inversely related to the size of the sample (large samples = smaller errors) 3. Parameter: characteristics of the entire population 4. Statistic: characteristic of a sample that is used to estimate the value of the population parameter |
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Misuse of Statistics
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- Misleading...
1. Questionable definition of terms (most, up to, trend) 2. Non-random and/or small samples 3.Biased researchers who could profit from results (supplement companies paying for results) 4. Misuse out of their intended context (only reporting a small portion) 5. Average is misleading. You have more than half of the scores above the average, when some scores are extremely low |
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Rank Order Distribution
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- Bigger amount of people, then you cant really use rank order really
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Normal Curve
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- Karl Gauss
- Referred to as Gaussian curve - The normal distribution forms the basis of all statistical inference - Characterized by symmetrical distribution of data about the center of the curve, not all symmetric curves are normal. - The mean (avg) median (50th percentile) and mode (score with highest frequency) are all in the center of the curve - Frequency of scores declines in a Predictable manner as the scores deviate farther from the center of the curve |
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Bell-shaped curve
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- with more people you can create a normal curve
- Not all bell-shaped curves are normal, but all normal curves are bell shaped. |
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Bimodial Curves
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- A curve with two modes, or peaks
- Major and minor modes may be identified |
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Skewed Curves
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- Formed when a disproportionate number of subjects score toward one end of the scale
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Positive Skew
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- Skewed curves
- The mode of the curve is pushed to the left (lower end) and the right tail is longer and points in a positive direction |
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Mesokurtic
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- Skewed curve
- Middle curve - Bell shaped |
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Leptokurtic curve
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- Skewed curve
- limited range wit most scores near the means |
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Platykurtic Curve
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- Skewed curve
- wide range of scores with low frequencies in the midrange of the curve |
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Percent
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- By the hundreds
- cent is latin root word for one hundred |
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Percentage
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- part of a whole expressed in hundredths
- provides the score's relation to the total possible score |
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Percentile
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- %ile
- The fraction, in hundredths, of the ordered scores that are < or equal to a give raw score. - 75th percentile means that 75 % of the scores are less than or equal to that score. - 34% of data is between the 2 lines (the mean and the first SD) |
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Standard Scores
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- A score derived from raw data and that has a known basis for comparison such as central tendency (mean) and variability (range)
- Allow the evaluation of raw scores and the comparison of two sets of data tat have different units of measurement. |
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Raw Score
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- data from measurements
- Dont provide as much information as the %iles. |
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Caution when using Percentiles
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- When the error in a measure is relatively large, it would be inappropriate to report an exact %ile rank, as the score is only an approximation
- Quartiles may be used - Ceiling Effect: there will be a lower %ile increase at the higher end of the scale for the same raw score inc in other parts of the scale. -- Caused by the plateau of the normal curve -- Consider this when providing grades, incentives and evaluations |
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Calculating Percentiles
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1. Rank Order distribution
2. Simple Frequency Distributions 3. Grouped f distribution |
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Rank Order Distribution
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- What % of scores falls at or below the level being sought
- %ile = (N scores < or equal x) / N * 100 |
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Simple Frequency Distributions
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- Using a cumulative f column
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Measures of Central Tendency
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- Values that describe the middle, or central, characteristics if a set of data
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Mode
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- The score that occurs most frequently in a distribution
- Pros: Ease of calculations and use with nominal data - Cons: disregards extreme scores and is a terminal statistic - USE IF: -- Rough estimates of C.T. is needed -- only measure of CT for nominal data -- Not much info |
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Terminal Statistic
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- Statistic that can not be used for further calculations
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Median
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- Score at the 50th percentile, or the middle score; divides the data set in half
- Based on the # of scores, not their value, therefore more appropriate for ordinal or highly skewed data - An outlier does not skew the median - Does not take the "value" of scores into account (therefore some information is lost) - USE IF -- Ordinal data -- The curve is badly skewed |
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Calculating the Median
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- In a set of rank ordered data where N is odd the median is the middle score
- When N is even the median falls between two scores and is either -- The higher of the 2 scores (ordinal data) -- The average of the 2 scores (interval or ratio data) |
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Mean
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- Arthmetic average
- Most common measure of central tendency - CONSIDERS BOTH THE # OF SCORES AND THEIR VALUES - Gives weight to each score according to its value or distance from the other scores - Most sensitive measure of central tendency - Appropriate for ratio and interval data however not for ordinal data. - Most sensitive measure of C.T., because of outliers - USE IF -- Interval or ratio data -- Normal distribution -- Both order and relitive value are important --Further calculations are to be made (really this one) |
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Outliers
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- Scores that are considerably higher or lower than the other scores
-- These can pull the mean toward the extremes -- Remember the positively skewed curve |
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Calculating the Mean
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- The sum of the variable scores (X), divided by the total number of scores (N)
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Positively Skewed Curve
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- Curve towards the left side
- Order: Mode, Median, Mean |
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Negatively Skewed Curve
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- Curve towards the right side
- Order: Mean, Median, Mean |
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Variability
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- A measure of the spread, or dispersion of a set of data
- Two or more, sets of data can be compared by means, but it may be more important to compare variability of the data. |
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Types of Variability Measures
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1. Range
2. Interquartile Range 3. Variance 4. Standard Deviation |
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Range
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- (R)
- High to low score - a quick, rough estimate of variability - Unstable when outliers are in the data set |
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Interquartile Range
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- (IQR)
- Difference between the raw scores at the 75th and 25th percentiles - IQR = Q3 - Q1 -- Used with ordinal data, or highly skewed ratio or interval data -- Only considers 50% of the data, or the middle half -- Like the Median, it is not affected by outliers. |
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Variance
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- (V)
- The average of the squared deviations from the mean; considers each score and its distance from the mean - It is not right score so not used in a lot of research |
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Deviation
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- (d)
- distance of each raw score from the mean - Considers the value of each data point - The sum of all deviations must be zero |
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Standard Deviation
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- SD
- The square root of the Variance, or square root of the avg of the squared deviations from the mean -- The variance is out of line with the original raw data, so the square root of the variance is computed --- The resulting value is now in alignment with the original raw data. - Many advanced statistics use X for central tendency and SD for dispersion |
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Standard Deviation of a Population
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1. Definition Method
2. The Raw score method |
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Standard Deviation of a Sample
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1. Samples rarely contain the extreme values of a population, thus, the variance of a sample is almost never as large as the population variance.
2. We use a correction factor so that the population estimate is not biased by a small sample 3. Degrees of Freedom (Df) : the # of values in a data set that are free to vary. When we estimate a value of a population from a sample (Parameter) we are putting limits on the data - Normal: the N is large, and the distribution of the data is "normal," there are 6 standard deviations within the range of data points; 3 below and tree above x. |
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Standardized Scores
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- Used to compare similar or dissimilar performances.
- Percentiles are an example of such standardized scales |
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Normal Curve and Standardized Scores
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- Many variables will assume a normal distribution if enough cases are observed, also nearly all physiological phenomenon
- Data must be from an interval or ratio scle |
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Z-scores
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- A raw score expressed in standard deviation units
- The percentage of the area under the normal curve between the x and any z score is constant and can be calculated. - 34.14% of the scores in a normal distribution lie between the mean and one z score +/-, therefore 68.28% of a popualtion lies between +/- 1 z score |
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Confidence Interval
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- 1.96 +/- is 95% exactly around the mean.
- 2.5 +/- 98% - 49.87% if the scores lie between the x and 3 SD or 99.74% lie +/- 3 SD from the x |
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Predicting Population Parameters
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- population is too big, therefore researcher assumes the sample represents the pop.
-- must be random and as large as possible (keep in mind resources) - Sample size limits: time, willingness of subjects, funds, equipment, facilities, etc. -- skinfolds are fast, inexpensive, field technique and valid -- UWW is $$, and time consuming. - Snowball samplling |
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Estimating Sample Error
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- Amount of error in the estimate of a parameter that is based on a sample statistic - pop estimate
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Standard Error of the Mean
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- A numeric value that indicates the amount of error that may occur when a random ample mean is used as a predictor of the the population mean
- The larger the sample, the smaller the error in predicting the pop mean. - If all the sample means (x) were then arranged in a frequency curve, the curve would approx a normal curve |
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The Central Limit Theory
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- The means from a series of samples randomly selected from a pop. will be normally distributed even if the pop. They were chosen from is not normal.
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The Grand Mean
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The mean of the means
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Pearsons product moment correlation coefficient (r)
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- Always between -1 and +1
- if r =0 no relationship - Sign of the coefficient does NOT indicate the strength or usefulness of the relationship coefficient - Sometimes the true line of best fit is curvilinear, not straight, and not correctly measured by Pearson's r! - Correlations have nothing to do with cause and effect. |
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Correlation
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- it is a inferential statistic, it simply states a relationship between variables
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R values
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- 7< r < .85
- The significance of r, the overall usefullness of the r value is based on size and significance is based on the size and significance |
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Common Variance
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(r squared)
- The amount of the variance in Y that can be explained by the variance in x - AKA the coefficient of determination |
