Craig W. Johnson, Ph.D.
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Observed Frequencies | |||
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| Meaning: | In both the chi-squre goodness of fit test and the the chi-square test of independence, also known as the chi-square test for contingency tables, tables are constructed showing the observed counts of data items within each cell of the table. These counts are called observed frequencies and represented as Oj, for the goodness of fit test, or Oij for the chi-square test of independence. They represent how many individuals, subjects, entities, etc. from the total data set are actually observed to fall within each of the different cells of the table. In other words, the observed frequencies constitute the raw data of the chi-square tests. | |||
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Related Term(s): | Chi-square Tests Marginal Frequencies Inferential Statistics Kruskal-Wallis Test Marginal Frequencies Nonparametric Observed Frequencies Wilcoxon Signed-Ranks Test | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Ordinal Scales | |||
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| Meaning: | Ordinal scales, the second level of measurement, and the lowest level typically used to measure quantitative variables, typically are used to order, or rank values of variables in addition to naming the values. Ordinal scales have all the characteristics of nominal scales but in addition, order or rank the data. Consequently, ordinal scales allow "less than" or "greater than" assessments to be made among the values of a variable. | |||
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Related Term(s): | Interval Scales Level of Measurement Nominal Scales Qualitative Variable Ratio Scales Types of Variables Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Parameter | |||
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| Meaning: |
A parameter formally is any value computed from a population.
Parameters are
always represented mathematically by greek
letters, (e.g.,
 ,
,2,
etc.).
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Related Term(s): | Population Sample Statistic | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Parametric Tests | |||
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| Meaning: | Parametic statistical procedures are inferential statistical methods designed to be used with normally distributed quantitative (interval or ratio) measures. Examples of parametric procedures include the t- Tests, and the Pearson Correlation Coefficient. | |||
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Related Term(s): | Chi-square Tests Inferential Statistics Nonparametric Population t-Tests. | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Percentile Rank | |||
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| Meaning: | The percentile rank for any data value is the percentage of scores at or below that value (i.e., 100(rcf) or 100(cf/N)). In other words it is 100 times the relative cumulative frequency. | |||
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Related Term(s): | Binomial Distribution Poisson Distribution Quantiles Relative Frequency Relative Cumulative Frequency Sampling Distribution Standard Deviation Standard Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Poisson Distribution | |||
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| Meaning: | The family of Poisson distributions is a category of discrete frequency distributions like the binomial distribution showing distributions of events having two possible outcomes, like success or failure. But, unlike the binomial distribution, it requires not two but just one parameter to compute probabilities. It turns out that this means the clinician can quickly use it as a simple method to closely approximate the binomial distribution for distributions of rare events (i.e., distributions where there are very many events, but the probability associated with a specific dichotomous outcome on any one event is small - like begin struck by lightening). | |||
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Related Term(s): | Binomial Distribution Gaussian Distribution | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Population | |||
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| Meaning: | A population is a collection of objects, events or individuals having characteristics that a researcher may be interested in studying. To study a population, the researcher typically selects a small group, called a sample, from the population. | |||
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Related Term(s): | Power Random Sample Sample Sampling Distribution | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Power | |||
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| Meaning: | Statistical power, or just "power", is the probability of rejecting the Null Hypothesis when it is false. In other words, when a relationship exists between the independent and dependent variables in the Population, statistical power measures the probability of detecting that relationship from the sample data. | |||
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Related Term(s): | Dependent Variables Independent Variables Null Hypothesis Statistical Significance | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Probability | |||
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| Meaning: | The probability of an event quantitatively describes the chances that the event will occur. Given a large number of different events the probability of an event is equal to the number of times the event occurs divided by the total number of events, or the relative frequency of the event. | |||
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Related Term(s): | Relative frequency Relative Cumulative frequency | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Qualitative Variables | |||
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| Meaning: | Qualitative variables are those variables which can be named, classified or categorized only and thus measured on nominal scales. | |||
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Related Term(s): | Continuous Variables Discrete Variables Interval Scales Level of Measurement Nominal Scales Ordinal Scales Quantitative Variables Ratio Scales Types of Variables Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Quantiles | |||
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| Meaning: | Centiles, deciles and quartiles are examples of quantiles. In general the i'th centile in a distribution is the data value having a percentile rank of i. Quantiles in frequency distributions are somewhat like quarters, dimes and cents with money. Just as there are 4 quarters, 10 dimes and 100 cents in a dollar; there are 4 quartiles, 10 deciles and 100 centiles in a frequency distribution. | |||
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Related Term(s): | Binomial Distribution Percentile Rank Poisson Distribution Relative Frequency Relative Cumulative Frequency Sampling Distribution Standard Deviation Standard Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Quantitative Variables | |||
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| Meaning: | Quantitative variables are variables for which "less than" and "greater than" relationships are meaningful. These variables are typically measured on either ordinal scales, interval scales, or ratio scales. . | |||
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Related Term(s): | Continuous Variables Discrete Variables Interval Scales Level of Measurement Nominal Scales Ordinal Scales Qualitative Variables Ratio Scales Types of Variables Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Random Sample | |||
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| Meaning: | A random sample is a sample chosen from a population in a fashion that ensures every object, event, item or individual has an equal chance of being drawn. The selection of any one entity can in no way influence or affect the selection of any other. Most statistical inferential procedures assume that researchers use random samples. The validity of such procedures rests upon the assumption that samples are genuinely representative random samples from populations. | |||
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Related Term(s): | Population Sample Sampling Distribution | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Range | |||
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| Meaning: | The range of a distribution is one of the simplest measures of variability of a distribution. It is simply the difference between the maximum and minimum values in the distribution. | |||
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Related Term(s): | Interquartile Range Mean Deviation Standard Error Standard Deviation Sum of Squares Variability | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Ranks | |||
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| Meaning: | Nonparametric statistical procedures often employ a procedure of ordering or ranking all data values in a single ordered series from the lowest to the highest (or vice versa). This procedure is equivalent to assigning ranks to data values (e.g, lowest has rank 1, next lowest has rank 2, next lowest has rank 3, etc.). Formulas exist for various nonparametric procedures which then can be applied to the ranks. Examples of procedures including such formulas include the Mann-Whitney U-test, the Wilcoxon signed-ranks test, the Krusal_Wallis test, and the Spearman rank correlation coefficient. | |||
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Related Term(s): | Nonparametric Statistics Ordinal Scales | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Ratio Scales | |||
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| Meaning: | Ratio scales, the fourth and highest level of measurement, have all the properties of interval scales, but in addition have the property that the ratio scale has a meaningful absolute zero. The 'zero' is not arbitrary, as in the case of interval scales (e.g., fahrenheit and celsius temperature scales), but represents the complete absence of any amount of the variable. | |||
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Related Term(s): | Interval Scales Level of Measurement Nominal Scales Ordinal Scales Qualitative Variable Types of Variables Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Regression Analysis | |||
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| Meaning: | Regression analysis is an inferential statistical method that develops equations from empirical random samples to make predictions about the values of a dependent variable based on the values of one or more independent variables with known probabilities of accuracy. It then tests significance of independent variables entered into the regression equation. Each independent variable has a coefficient in the equation called a regression coefficient. The equation also has a constant term called the regression constant or just the constant term. If there is more than one independent variable which may be entered into the equation the method is referred to as "multiple regression". | |||
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Related Term(s): | Criterion Variable Dependent Variable Independent Variable Linear Regression Predictor Variable Residual Types of Variables Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Relative Frequency | |||
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| Meaning: | The relative frequency (rf) of a data value is simply the frequency of the value divided by the total number of data values. In other words, the relative frequency is the fraction of data values or scores having the given value. | |||
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Related Term(s): | Binomial Distribution Cumulative Frequency Percentile Rank Poisson Distribution Relative Cumulative Frequency Sampling Distribution Standard Deviation Standard Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Relative Cumulative Frequency | |||
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| Meaning: | The relative cumulative frequency (rcf) of a data value is simply the cumulative frequency of the value divided by the total number of data values. In other words, the relative cumulative frequency is the fraction of data values or scores at or below the given value. | |||
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Related Term(s): | Binomial Distribution Cumulative Frequency Poisson Distribution Relative Frequency Sampling Distribution Standard Deviation Standard Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Relationships among Variables | |||
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| Meaning: | Scientific research investigates relationships among variables. Such relationships take the form that as one variable increases another tends to increase, or as one variable increases another tends to decrease. Theses relationships may be causal, meaning that the changes in one variable depend on the changes in another; or they may be correlational, meaning that the variables tend to change at the same time, but there is not necessarily a causal relationship between the two variables. The relationship between the foot size and vocabulary in a population of grade school students provides an example of a non-causal correlational relationship. | |||
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Related Term(s): | Causal Relationship Scientific Research Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Reliability | |||
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| Meaning: | An instrument is said to be reliable if it consistently reports the same measure for the same quantity of the measured variable. Reliability is typically measured with a reliability coefficient obtained by computing a correlation coefficient. | |||
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Related Term(s): | Coefficient Alpha Reliability Correlation Equivalent Forms Reliability Split-half Reliability Test-Retest Reliability Measurement Validity | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Research Hypothesis | |||
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| Meaning: | The research hypothesis is also called the alternative hypothesis. It is the opposite of the null hypothesis. The research hypothesis states there is a relationship between the independent and dependent variables. When the null hypothesis is rejected, based on research data, it implies acceptance of the research hypothesis. The research question is simply the research hypothesis put in the form of a question rather than a statement. | |||
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Related Term(s): | Alpha Inferential Statistics Null Hypothesis Population Power. | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Residual | |||
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| Meaning: | A residual is the difference between the predicted value (often from a regression equation) and the actual or observed value. Examination of residuals in regression analysis will identify atypical cases. | |||
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Related Term(s): | Regression Analysis | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Robust | |||
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| Meaning: | A statistical test is said to be robust under the violation of certain designated assumptions if the test remains valid (conclusions are true within prescribed approximate error limits (e.g., alpha) under those conditions. | |||
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Related Term(s): | Alpha | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Sample | |||
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| Meaning: | A sample is a collection of objects, events or individuals selected from a population, typically in some systematic fashion. A researcher selects a sample to study and make inferences about a population. | |||
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Related Term(s): | Population Power Random Sample Sampling Distribution | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Sample Size | |||
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| Meaning: | Sample size is the number of subjects (people, plants, etc.) in a group selected from a population. Because sampling error tends to be smaller for larger samples, larger samples have more statistical power. | |||
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Related Term(s): | Power Population. Sampling Distribution Standard Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Sampling Distribution | |||
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| Meaning: | Whenever random samples of a given size are taken repeatedly from a population of scores and a statistic (e.g., the mean) is computed for each sample, the distribution of this computed statistic may be constructed. The resulting distribution is called a sampling distribution (e.g., the sampling distribution of the mean). | |||
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Related Term(s): | Population. Random Sample | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Scatterplot | |||
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| Meaning: |
Scatterplots, scatter diagrams or scattergrams are graphs
of pairs of data values showing the locations of
points representing the data values. Such graphs
are used to explore relationships among the variables
and to determine whether any curvilinear trends may
be present in the data. A glance at a scatterplot
may quickly tell whether the Pearson or Spearman
correlations are appropriate measures of relationship
for the data. Nonlinear trends in the data may
be visually apparent as curved patterns in the graph.
See example below:
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| A Scatterplot | ||||
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Related Term(s): | Correlation. Variable | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Scientific Research | |||
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| Meaning: | Scientific research is the systematic and empirical study of relationships among variables. | |||
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Related Term(s): | Empirical. Relationships Among Variables Variables | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Semi-Interquartile Range | |||
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| Meaning: | The semi-interquartile range is half the interquartile range. | |||
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Related Term(s): | Interquartile Range Mean Deviation Range Standard Error Standard Deviation Sum of Squares Variability Variance | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Statistical Significance | |||
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| Meaning: | The statistical significance, or level of significance, is the probability of rejecting a true null hypothesis. That is, it is the probability that an investigator will conclude that a relationship exists between the independent and dependent variables when no such relationship exists, a false positive. It is represented by the lowercase Greek letter alpha. | |||
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Related Term(s): | Alpha Null Hypothesis | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Skewness | |||
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| Meaning: | A distribution that is not symmetric is skewed. That is, a skewed distribution is a lopsided distribution. In such distributions the mean, median and mode are typically all different. The more lopsided the distribution is the more skewed it is. | |||
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Related Term(s): | Box Plot Distribution Exploratory Data Analysis Kurtosis Normal Distribution | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Split-Half Reliability | |||
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| Meaning: | Split-half reliability is employed when scores from two halves of the same instrument are correlated. | |||
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Related Term(s): | Coefficient Alpha Reliability Correlation Equivalent Forms Reliability Reliability Test-Retest Reliability Measurement Validity | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Standard Deviation | |||
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| Meaning: | The standard deviation is a measure of variability. It provides a measure that can be thought of as being the "average distance" that values are from the Mean. It is expressed in the same units as the original values. Mathematically it is computed as the square root of the average squared distance from the mean of the values. | |||
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Related Term(s): | Interquartile Range Mean Deviation Population Range Standard Error Sum of Squares Variability Variance | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Standard Error | |||
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| Meaning: | The standard error of any statistic is the standard deviation of its sampling distribution. You can find an estimate of the standard error of the mean by dividing the standard deviation by the square root of the sample size. | |||
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Related Term(s): | Mean Sampling Distribution Standard Deviation Variability Variance | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Standard Normal Distribution | |||
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| Meaning: | The standard normal distribution is a special normal distribution that has relative frequencies on the vertical axis and has a mean of zero and a standard deviation of one. It has z-scores on the horizontal axis. Tables of the standard normal distribution show the areas under the normal curve associated with the points along the z axis. | |||
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Related Term(s): | Gaussian Distribution Mean Sampling Distribution Standard Deviation z-Scores | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Statistic | |||
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| Meaning: | A statistic formally is any value computed from a sample selected from some larger population. Statistics are always represented mathematically by conventional english letters, (e.g., S, S2, M, etc.). Test statistics (e.g., F, t, z, etc.) are often tabled for easy access because of frequent usage. | |||
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Related Term(s): | Parameter Population Sample | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Sum of Squares | |||
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| Meaning: | The sum of squares (SS) is a measure of variability. Mathematically is is computed as the sum of the squared deviations of the data values from the Mean. In the analysis of variance different sums of squares are computed for each different source of variability (e.g., SSB, SSW). | |||
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Related Term(s): | Interquartile Range Mean Deviation Population Range Standard Deviation Standard Error Variability | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Summary Statistics | |||
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| Meaning: | Summary statistics or descriptive statistics concern that branch of statistics that has as its primary focus summarizing data from groups. Such statistics enable investigators to describe with precision a collection of quantitative information in a manner that is concise, convenient, easily interpreted, and easy to communicate. For example, a clinician might choose to use the mean to summarize a large number of patients'. EXAMPLES: mean, median, mode, standard deviation, z-score. | |||
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Related Term(s): | Inferential Statistics Mean Population. Standard Deviation | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Test-Retest Reliability | |||
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| Meaning: | Test-retest reliability is employed when scores obtained from two administrations of an instrument are correlated. | |||
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Related Term(s): | Coefficient Alpha Reliability Correlation Equivalent Forms Reliability Reliability Split-Half Reliability Measurement Validity | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
t-Test | |||
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| Meaning: | t-Tests are used to detect significant differences in means of quantitative variables. The t-tests generally require the data to be normally distributed and from populations having equal variability unless samples sizes are approximately equal. Tests have the above characteristics are frequently referred to as parametric tests. There are three t-tests, the t-test for independent samples, for paired-samples and for the mean of a single sample. | |||
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Related Term(s): | Chi-square Tests Inferential Statistics Population. | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Table of Contents | |||
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| Meaning: | A lesson Table of Contents introduces each Essential Research Statistics for the Health and Behavioral Sciences lesson. The Table of Contents can be used to identify the content of the lesson and to choose and move to a particular section within the lesson. To choose and move to any section, simply move the cursor to the underlined line containing the topic to be selected and click the mouse button. The Table of Contents names the major sections covered within the chosen lesson. | |||
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Related Term(s): | Instructions Lesson | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Type I Error | |||
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| Meaning: | A Type I error occurs when a true null hypothesis is rejected. In lay language this could be described as a "false alarm" or a false positive. The experimenter concludes there is an effect when in fact there is none. The probability of a Type I error is represented by the lowercase Greek letter alpha. So, alpha is the probability of rejecting a true null hypothesis. | |||
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Related Term(s): | Alpha Beta Null Hypothesis Statistical Significance Type II Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Type II Error | |||
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| Meaning: | A Type II error occurs when a false null hypothesis is retained or accepted. In lay language this could be described as a false negative. The experimenter concludes there is no effect when in fact there is. The probability of a Type II error is represented by the lowercase Greek letter beta. So, beta is the probability of retaining a false null hypothesis. | |||
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Related Term(s): | Alpha Beta Null Hypothesis Statistical Significance Type I Error | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Types of Variables | |||
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| Meaning: | Types of variables refers to the several different and important classifications of variables which are most essential to know in order to understand and appropriately use the most important and frequently used statistical methods (e.g., independent vs. dependent, qualitative vs. quantitative, continuous vs. discrete. | |||
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Related Term(s): | Continuous Variables Discrete Variables Dependent Variables Independent Variables Interval Scales Nominal Scales Ordinal Scales Qualitative Variables Quantitative Variables Ratio Scales Variables | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Variables | |||
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| Meaning: | The variable is the fundamental entity studied in scientific research. A variable is an attribute or thing which is free to vary (can take on more than one value). | |||
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Related Term(s): | Types of Variables | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Variability | |||
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| Meaning: | Variability, deviation, dispersion, concentration or degree of scatter of data values is one of the central concepts of statistics. Variability has to do with how dispersed the data values are, how much distance there is between the data values, how spread out they are. There are many measures of variability. Some of the most important are the range, the interquartile range and the standard deviation. | |||
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Related Term(s): | Interquartile Range Population Range Standard Deviation Standard Error Variance | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Variance | |||
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| Meaning: | The variance is an excellent measure of variability. Mathematically you compute it by dividing the sum of squares (SS) by either N or N - 1, depending upon whether you have a population or a sample from a population and wish to use the sample value as an estimate of the population value. | |||
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Related Term(s): | Interquartile Range Mean Deviation Population Range Standard Error Sum of Squares Variability | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
Wilcoxon Signed-Ranks Test | |||
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| Meaning: | The Wilcoxon signed-ranks test is a nonparametric alternative to the dependent t-test. It is used with two dependent samples measured on at least ordinal scales applied to continuous variables. | |||
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Related Term(s): | Chi-square Tests Inferential Statistics Kruskal-Wallis Test Mann-Whitney U-Test Nonparametric | |||
Essential Research Statistics for the Health and Behavioral Sciences
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| Term: |
z-Score | |||
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| Meaning: | For every data value measured on interval or ratio scales there is a corresponding z-score. Mathematically you compute the z-score by subtracting the mean from the data value and dividing the difference between the data value and the mean by the standard deviation of the distribution. The z-score then measures the distance the data value is from the mean in standard deviation units. z-scores are sometimes called standard scores. But, there are other types of standard scores as well. | |||
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Related Term(s): | Mean Standard Deviation Standard Error Sum of Squares Variability | |||