Objectives for Unit One
1. Know the meaning
and recognize examples of a variable and variable value.
A variable is a quantity of number that may change in various circumstances. The actual quantity itself is called the value of the variable.
2. Know the meaning
and recognize examples of a population and sample.
A population is a complete set of objects or observations which have some common observable characteristic. A sample is a subset of a population. The subset may range in size from one element or observation to the complete population.
3. Know the meaning
and recognize characteristics and examples of parameters and statistics.
Parameter are characteristics of populations. They are stable, fixed, and unvarying. Statistics are characteristics of samples. They fluctuate from one sample to another.
4. Know the meaning
of a descriptive value and an inference.
A descriptive value is a number that describes a population or a sample. A parameter is a descriptive value of a population and a statistic is a descriptive value of a sample. An inference in statistics is an estimate of a population parameter value based on a statistic computed from a sample taken from the population of interest. The estimate frequently contains an estimate of the error likely to occur expressed in terms of a range of values within which the parameter is likely to occur and a probability associated with the estimate.
5. Know the letters
used to indicate parameters and statistics.
Parameters are symbolized by Greek letter (, , etc.). Statistics are symbolized by Roman letters (p, s, etc.)
6. Know the meaning
and recognize examples of nominal, ordinal, interval and ratio scales of
A nominal scale is when the values given to observations are qualitative and have no quantitative significance. Different numbers assigned to objects or observations cannot be compared as being higher or lower, only as being the same or different. The numbers one, two, and three are different but one cannot be considered to be higher or lower than two or three in a nominal scale.
An ordinal scale is when the values given to observations signify the order or rank of the data from high to low, but the difference between the values is not meaningful. The number one is lower than two which is lower than three, but the difference between one and two is not the same as the difference between two and three in an ordinal scale.
An interval scale is when the values given to observations reflect true differences between the values and arithmetic operations can be done with the values. The difference between one and two is the same as the difference between two and three in an interval scale.
A ratio scale is when the values given to observations are based on a scale in which zero means absence of any of the characteristic and ratios can be meaningfully made. Four is twice as much as two in a ratio scale.
7. Know the
meaning and recognize examples of qualitative and quantitative variables.
Quantitative variables are measured in such a way that statements indicating the amount of difference between two variable values can be made. Statements about qualitative variables can only indicate difference between values or that one value is more or less than the other, but no indication of the amount of the difference. Qualitative variables are measured on a nominal or ordinal scale while quantitative variables are measured on an interval or ratio scale.
8. Know the meaning
and recognize examples of independent and dependent variables.
Independent variables are variables that are either controlled or manipulated by the researcher or used to classify data. They are considered to be the causes of the effects to be studied. The dependent variable measures the effect of the independent variable.
9. Know the meaning
and recognize examples of continuous, discrete, and discrete approximation
to continuous numbers (or variables).
Discrete numbers can only fall at certain separated points on a scale while continuous numbers can have any possible value on the scale (within the top and bottom limits, if any). On a continuous scale, you can always find a number between any other two given numbers. On a discrete scale, there are numbers that cannot exist. In statistics, most variables are considered to be continuous, and the numbers used in their measurement are discrete approximations of the true continuous value, since the measurement instruments are seldom, if ever, precise enough to find the true value.