Observation, measurement and statistics are the basis of science and common sense. Statistics are used to collect, organize, analyze and interpret numerical data.

Critical evaluation of research involves the understanding of and assessment of the degree to which the statistics are appropriately applied. Results can be interpreted (and misinterpreted) depending on the statistics used.

Statistical terms are a language or system of communication . This NOTE includes definitions of some of the most common statistical concepts. There is repetition of terms when useful in defining another term. It will be useful when reading Note #B9. Refer to books on statistics found in Horizon, the Busse Library catalog, for more detailed information.

applied research – research done with the hope that the findings will have practical applications

basic research – research done to expand knowledge about a phenomenon

bias (sample bias) – when the observations or measurements do not accurately represent the intended population

central tendency - the description of the average or typical value of the group. The three types are: mean, median and mode.

confidence interval - the range in which the true measurement is likely to fall at a specified level of probability.

confounding factor – a variable which may or may not be one of the independent variables but does affect the variables in the study, thus making it difficult to decide whether the independent variable or an extraneous variable caused the outcome effect

control group – an untreated group in an experimental study that is used to compare with the treated group

correlation – the degree to which two measurements relate to one another; not cause and effect but their relative positions, one to the other. The two measures may be positive +1.0 (increase or decrease together) or negative -1.0 (one increases while the other decreases). Most correlations fall between the two extremes. Correlations near zero indicate little or no relationship between the variables. Another way to define correlation: the degree to which two events occur together. The relationship is the coefficient and lies between +1 and -1. When one type of measurement increases while another decreases, they are said to have a negative correlation. When the direction of change is the same the two measurements are positively correlated. 

data – the numerical information when measuring a variable

• discrete data – scores are whole numbers with whole unit intervals: 1, 2, 3, 4 (eg. size of family)

• continuous data – when scores can be anywhere along a range including decimals from lowest to highest acceptable for that variable: 1, 1.25, 7, 9.15 (eg. response time in seconds)

descriptive research – non-experimental attempt to describe what exists without manipulations of the variables. Data analysis may lead to hypotheses for testing in experimental studies.

descriptive statistics -  a summary of the data set that describes the characteristics of a sample including measures of central tendency, measures of variablity, frequency counts, correlation etc.

empirical – based on observation or experimentation

empirical study – one of several types of observational research

• hypothesis-testing study – designed to test or evaluate one or more hypotheses that are constructed before the research is designed
  • correlational study – determine how variables in the study move in relation to one another; not necessarily cause and effect
  • predictive study - determine whether one or more variables can predict another variable, based on their relationships
  • experimental study – to see the impact of a treatment (independent variable) on a dependent variable; to establish causal relations

• descriptive study – to describe a set of characteristics, conditions, situations from which ideas for hypothesis testing can be garnered
  • case study - gathering and reporting observations on single individuals or very small groups

frequency distribution – one of the ways of describing a pattern within a trait

graph - a visual representation of data or results as lines, bars or points

hypothesis – a statement about the correlational, predictive or causal relationship between the variables to be studied

• research hypothesis - a statement of proposed differences between the groups or treatments

• null hypothesis – one way of stating a hypothesis; that there are no differences between two or more groups for the variables to be studied, after which the experimenter tries to determine if this is so
  • Type I error – probability of rejecting the null hypothesis when it is true – claiming a difference when there is no difference
  • Type II error – probability of accepting null hypothesis when it is false – failing to detect a real difference when there is one

independent variable - intervention which influences or causes change in dependent variable. 

inferential statistics – using the sample (observations of a small group of subjects) to make inferences about a larger group, the population OR the statistics used to predict the unknown from the known or from the smaller group (sample) to larger (population).

measures of central tendency – the ways of describing the middle of a data set : mean, median, mode

• mean  (m) – the sum of the actual values along a distribution divided by the number of values or data points; the arithmetic average

• median – the central observation above and below which half of the observations fall

• mode – the most common measurement or value in a sample

measures of variability – identify the amount or degree of scatter of a set of values (see also, variance)

• standard deviation – most frequently used; a measure of the spread of a group of values with two thirds of the values lying between ±1SD of the mean

• range – the difference between the largest and smallest values in a set of data

meta-analysis – the combining of several studies with sophisticated statistical methods and the reanalysis of the data with the larger sample size to determine the state of knowledge about those correlational, predictive and causal relationships

normal distribution, normal curve, bell curve – a mathematical description of frequency distribution of a set of values

null hypothesis - assumes that two means are not significantly different until means are tested and found to be statistically different

randomization – using a mathematical paradigm to assign subjects to treatment and non-treatment groups; is important in minimizing one form of bias

range – the difference between the highest and lowest value in the group of measurements

reasoning

• inductive reasoning approach – theory is generated by collecting observations that lead to a hypothesis that can be tested

• deductive reasoning approach – theory is generated from known facts, moving from the general to the specific; used to test predictions and validate existing relationships

research design -- a plan, based on the research question and research type, and previous research that may have been done (review of literature), of what data to gather, how and from where or whom and what statistical analyses will be applied. All these should be decided before research is begun.

research types – a study may involve one or more of these characteristics

• case study – a type of descriptive study where a limited number of subjects are studied in an attempt to ascertain what exists

• correlational study – determine how variables in the study are related to one another; not necessarily cause and effect; what is the relationship among the variables

• descriptive – attempt to ascertain what exists (see also, descriptive research)  Describe a set of characteristics, conditions, situations from which ideas for hypothesis testing can be generated

• experimental study –  to see the impact of a treatment (manipulated independent variable) on a dependent variable; to establish causal relationships (eg. cause-effect relationship)

• hypothesis-testing study – designed to test or evaluate one or more hypotheses that are constructed before the research is designed

• non-experimental study – another term for descriptive where no variables are manipulated and the setting is not controlled

• predictive study - to determine whether one or more variables can predict values of another variable

• quantitative study – generating knowledge by measuring amounts of the variables

• qualitative study – generating knowledge about the meaning (see also,  reasoning - inductive)

• quasi-experimental study – research design may involve manipulation of a subject but the treatment was not randomly assigned, thus more uncertainty exists about causal relationships

statistical significance – a difference that is real and reliable. The extent to which the results were not a chance occurrence, e.g. 8 heads and 2 tails are unlikely results when tossing a fair coin 10 times

statistics – a set of mathematical tools and procedures used to interpret information

• descriptive statistics – the data set that describe the characteristics of a sample; the observations that are going to be analyzed

• inferential statistics - used to predict the unknown from the known or from the smaller group (sample) to larger (population)

• parametric statistics – statistics used to to see if data is normally distributed

theory – an organized and systematic set of interrelated concepts that describe the relationship among a set of variables, for the purpose of understanding the nature of the whole

• inductive reasoning approach – theory is generated by collecting observations that lead to a hypothesis that can be tested

• deductive reasoning approach – theory is generated from known facts, moving from the general to the specific; used to test predictions and validate existing relationships

t-test - examines difference between means of 2 samples to determine how comparable the populations are

validity – extent to which the test measures what it is intended to measure; do they measure what they are supposed to?

• content validity – it measures all important parts of the concept

• predictive validity – measures events accurately

• concurrent validity – the differences found are accurate

• construct validity – measures the intended variable

variable – a measurable characteristic

• dependent – the variable(s) to be measured to see if changes in the independent variable(s) caused an effect

• independent – the variable(s) that may cause changes in the dependent variable(s)

• extraneous – one or more variables that are present and neither manipulated nor measured, that may affect the results

variance - degree to which each measurement deviates from the mean. The standard deviation of a data set, squared. An important statistic that is sometimes difficult to interpret. (see also, measures of variability)

x-axis – the horizontal line or set of values on a histogram

y-axis – the vertical line or set of values on a histogram