Chapter 1 Measurement, Statistics, and Research

What is Measurement? Measurement is the process of comparing a value to a standard Measurement is the process of comparing a value to a standard Statistics is a mathematical tool used for interpretation Statistics is a mathematical tool used for interpretation Precision is essential: if the measurement is not PRECISE, the results cannot be TRUSTED Precision is essential: if the measurement is not PRECISE, the results cannot be TRUSTED

What is Measurement? To be acceptable the data must be To be acceptable the data must be –Valid, Reliable & objective Valid (must be compared to known value or method) Valid (must be compared to known value or method) Reliable – is the measurement consistent? Reliable – is the measurement consistent? Objective – free from BIAS? Objective – free from BIAS?

Steps in Measurement Process 1. Object to be measured is identified and defined 2. The standard to which the object is to be compared is identified and defined 3. A comparison of the object to the standard is made 4. A quantitative statement of the relationship between the standard an object is made (statistical evaluation)

Variables and Constants A variable is a characteristic that can assume more than one value A variable is a characteristic that can assume more than one value A constant can assume only one value A constant can assume only one value

Types of Variables Continuous variable – can assume any value (ht, wt) Continuous variable – can assume any value (ht, wt) Discrete variable – limited to certain values: integers or whole numbers (2.5 children?) Discrete variable – limited to certain values: integers or whole numbers (2.5 children?)

Classification of Data or Level of Measurement Nominal Scale: mutually exclusive (male, female) Nominal Scale: mutually exclusive (male, female) Ordinal Scale: gives quantitative order to the variable, but it DOES NOT indicate how much better one score is than another (RPE of 2 is not twice of 1) Ordinal Scale: gives quantitative order to the variable, but it DOES NOT indicate how much better one score is than another (RPE of 2 is not twice of 1) Interval Scale: has equal units and zero is not an absence of the variable (temperature) Interval Scale: has equal units and zero is not an absence of the variable (temperature) Ratio Scale: based on order, has equal distance between scale points, and zero is an absence of value Ratio Scale: based on order, has equal distance between scale points, and zero is an absence of value

Research Design & Statistical Analysis Research is a technique for solving problems. Identifying the problem is critical Research is a technique for solving problems. Identifying the problem is critical Types of Research: Types of Research: –Historical –Descriptive –Experimental: involves manipulating and controlling variables to solve a problem Hypothesis: Hypothesis: –an educated guess –based on prior research –Can be tested

Hypothesis Testing Research Hypothesis (H 1 ): predicts relationships or differences between groups Research Hypothesis (H 1 ): predicts relationships or differences between groups Null Hypothesis (H 0 ): predicts NO relationship or differences between groups Null Hypothesis (H 0 ): predicts NO relationship or differences between groups The statistical analysis reports the PROBABILITY that the results would if H 0 were true The statistical analysis reports the PROBABILITY that the results would if H 0 were true If the probability (1 in 100) or (5 in 100) that the null is true, we REJECT the null and ACCEPT H 1 If the probability (1 in 100) or (5 in 100) that the null is true, we REJECT the null and ACCEPT H 1 NOTE: We never PROVED EITHER! NOTE: We never PROVED EITHER!

Independent & Dependent Variables Independent Variable: totally free to vary. (balance is independent of VO 2 ) Independent Variable: totally free to vary. (balance is independent of VO 2 ) Dependent Variable: NOT free to vary (ht and wt) Dependent Variable: NOT free to vary (ht and wt) The INDEPENDENT VARIABLE is controlled by the researcher (effects of on body fat) The INDEPENDENT VARIABLE is controlled by the researcher (effects of exercise on body fat) The DEPENDENT VARIABLE is the variable being studied (effects of exercise on body fat) The DEPENDENT VARIABLE is the variable being studied (effects of exercise on body fat)

Internal Validity Internal Validity: Internal Validity: –refers to the design of the study –All potential intervening variables must be controlled (rat studies are easier to control) –Failure to use a control group harms internal validity –Instrument Error reduces internal validity –Investigator Bias reduces internal validity

External Validity External Validity refers to the ability to generalize the results of a SAMPLE to the POPULATION (rat studies don’t always generalize to humans) External Validity refers to the ability to generalize the results of a SAMPLE to the POPULATION (rat studies don’t always generalize to humans) If a sample is not RANDOM it may not represent the population If a sample is not RANDOM it may not represent the population The process of generalizing from a SAMPLE to a POPULATION is statistical inference The process of generalizing from a SAMPLE to a POPULATION is statistical inference

Statistical Inference A Population is a group with a common characteristic A Population is a group with a common characteristic A population is usually large and it is difficult to measure all members A population is usually large and it is difficult to measure all members To make inference about a population we take a representative sample (RANDOM) To make inference about a population we take a representative sample (RANDOM) In a random sample each member of the population is equally likely to be selected In a random sample each member of the population is equally likely to be selected A stratified sample is a sample that is selected according to existing subcategories (rep, dem, ind) A stratified sample is a sample that is selected according to existing subcategories (rep, dem, ind) A sample cannot accurately represent the population unless it is drawn without BIAS A sample cannot accurately represent the population unless it is drawn without BIAS In a bias free sample selection of one member does not affect to selection of future subjects In a bias free sample selection of one member does not affect to selection of future subjects

Parameters and Statistics A parameter represents the population A parameter represents the population A statistic represents the sample A statistic represents the sample The difference between a statistic and a parameter is the result of sampling error The difference between a statistic and a parameter is the result of sampling error

Probability and Hypothesis Testing Statistics is the science of making educated guesses Statistics is the science of making educated guesses Statistics allow us to make a statement and then cite the odds that it is correct Statistics allow us to make a statement and then cite the odds that it is correct A random sample of 200 females have a mean ht of 5’ 2” ± 2”. The odds are 95 to 5 that this mean is correct. A random sample of 200 females have a mean ht of 5’ 2” ± 2”. The odds are 95 to 5 that this mean is correct.

Probability and Hypothesis Testing A random sample of 200 females have a mean ht of 5’ 2” ± 2”. A random sample of 200 females have a mean ht of 5’ 2” ± 2”. This means that the odds are 95 to 5 that the true mean is between 5’ and 5’ 4” This means that the odds are 95 to 5 that the true mean is between 5’ and 5’ 4” If a sample results in a mean of 5’ 3” we accept a hypothesis that the ht is 5’ 3” because it lies within the limits (5’ and 5’ 4”) If a sample results in a mean of 5’ 3” we accept a hypothesis that the ht is 5’ 3” because it lies within the limits (5’ and 5’ 4”)

Theories and Hypotheses A theory is a belief regarding a concept or a series of related concepts A theory is a belief regarding a concept or a series of related concepts Many hypotheses can be TESTED Many hypotheses can be TESTED If a sufficient number of results confirm the theory it is accepted as true If a sufficient number of results confirm the theory it is accepted as true Mental practice improves performance Mental practice improves performance

Misuse of Statistics Abdominal Exercise devices? Abdominal Exercise devices? Toothpaste? Toothpaste? Examples of statistics that may or may not be true Examples of statistics that may or may not be true Lack of random sample, small sample size, research is PAID Lack of random sample, small sample size, research is PAID Outliers: extreme scores (more than 3 SD) Outliers: extreme scores (more than 3 SD) Mean income (Income is a skewed distribution) Mean income (Income is a skewed distribution)