Module 1 Flashcards
Descriptive Statitistics
Descriptive statistics emphasizes simply describing the characteristics of a set of data. In other words, descriptive statistics is the tabular, graphical, and numerical summaries of data. (OpenStax, 2019)
Inferential Statistics
Inferential statistics allows us to make generalizations, estimates, forecasts, or other types of findings based on the data. For example, what if we were to try and summarize data on all residents of the United States?
While this wouldn’t be impossible, there are often time and cost limitations that don’t allow for data to be collected. In this case, instead of analyzing the entire population (the set of all elements of interest in a particular study), we look at a subset of the population known as a sample. This process of using data obtained from a sample to make estimates or test hypotheses about the characteristics of a population is called a statistical inference. (OpenStax, 2019)
Statistic
which is a number that represents a property of that sample
Parameter
which is a numerical characteristic of the whole population (OpenStax, 2019)
Random Sample
has the same characteristics as that population. When selecting a random sample, it is done so that every member of the population has an equal chance of being selected (OpenStax, 2019).
Simple Random Sampling
is a straightforward method for selecting a random sample; assign each member of the population a number. Use a random number generator to select a set of labels. These randomly selected labels identify the members of your sample (OpenStax, 2019).
Stratified Sampling
is a method for selecting a random sample used to ensure that subgroups of the population are represented adequately; divide the population into groups (strata). Use simple random sampling to identify a proportionate number of individuals from each stratum (OpenStax, 2019).
Cluster Sampling
is a method for selecting a random sample and dividing the population into groups (clusters); use simple random sampling to select a set of clusters. Every individual in the chosen clusters is included in the sample (OpenStax, 2019).
Systematic sampling
is a method for selecting a random sample. First, list the members of the population. Use simple random sampling to select a starting point in the population. Let k = (number of individuals in the population)/(number of individuals needed in the sample). Choose every kth individual in the list starting with the one that was randomly selected. If necessary, return to the beginning of the population list to complete selecting your sample (OpenStax, 2019).
Convenience Sampling
which is used to select individuals that are easily accessible and may result in biased data
Data
the facts and figures collected, analyzed, and summarized for presentation and interpretation
Data Set
All of the data collected in a particular study
Elements
are the entities on which data are collected.
Variable
is a characteristic of interest for the elements
Observation
The set of measurements obtained for a particular element
Categorical (qualitative) Variables
can be summarized by counting the number of people or objects that fall into a specific category (OpenStax, 2019). When someone places a person or object into a category, they are using a categorical measure.
Quantitative Variables
Make it possible to determine how much of something is present, not the category to which it belongs (OpenStax, 2019).
Discrete Quantitative Variables
can be only certain values in an interval with possible gaps in the interval that are not available. For instance, if you were to go to the store to buy tea, you would only be able to buy full boxes of tea. So, you could buy 1, 2, or 3 boxes, but you could not buy 1.5 boxes, since it does not come in half boxes
Continuous Quantitative Variables
can be any value within an interval. Here you can think about how much fuel is in your car’s gas tank. Depending on the accuracy of your measurement, it could be 12.1 gallons, 12.14 gallons, 12.142 gallons, or even 12.1424 gallons at any given moment. All values can be used in the measurement (OpenStax, 2019).
Nominal Level
consists of category names or numbers only to identify membership in a group or category (OpenStax, 2019).
Ordinal Level
consists of numbers to represent “greater than” or “less than” measurements in things such as rankings or preferences (OpenStax, 2019).
Interval Level
contains the ordinal level along with a unit of measurement that allows one to describe how much more or less one object has than another. In an interval level, there is no “true or absolute” 0 value. Temperature in degrees Fahrenheit or Celsius is an example of an interval level
Ratio Level
contains the interval level, but it also includes an absolute zero, and multiples have a meaning (OpenStax, 2019).
Frequency Distribution
is a table that shows classes of data and the number of cases in each class.
How are classes formed in a frequency distribution?
Classes are formed by specifying ranges that will be used to group the data
What is the goal of using classes in a frequency distribution?
The goal is to use enough classes to show the variation in the data, but not so many classes that some of them contain only a few data items.
How many classes should be used in a frequency distribution?
we recommend using between 5 and 20 classes. For a small number of data items, as few as 5 or 6 classes may be used to summarize the data. For a larger number of data items, a larger number of classes is usually required.
How to determine the width of a frequency distribution?
As a general guideline, we recommend that the width be the same for each class. Thus, the choices of the number of classes and the width of classes are not independent decisions. A larger number of classes means a smaller class width, and vice versa. To determine an approximate class width, we begin by identifying the largest and smallest data values. Then, with the desired number of classes specified, we can use the following expression to determine the approximate class width:
Approximate class width= largest data value - smallest data value/ number of classes
How to determine class limits in frequency distribution?
Class limits must be chosen so that each data item belongs to one and only one class. The lower-class limit identifies the smallest possible data value assigned to the class. The upper-class limit identifies the largest possible data value assigned to the class. In developing frequency distributions for categorical data, we did not need to specify class limits because each data item naturally fell into a separate class. But with quantitative data, class limits are necessary to determine where each data value belongs.
Relative Frequency
the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes (OpenStax, 2019). To find the relative frequencies, we must divide each frequency by the total number of students in the sample. Note that relative frequencies can be written as fractions, percentages, or decimals.
Cumulative Relative Frequency
the accumulation of the previous relative frequencies. We can find this frequency by adding all the previous relative frequencies to the relative frequency for the current row (OpenStax, 2019).
Outlier
an observation of data that does not fit the rest of the data.
Histogram
is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets (OpenStax, 2019).
Sampling
to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population.
Probability
a mathematical tool used to study randomness. It deals with the chance (the likelihood) of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails.
Population
a collection of persons, things, or objects under study.
representative sample
The sample must contain the characteristics of the population
Datum
a single value
Pareto chart
consists of bars that are sorted into order by category size (largest to smallest).
