Statistics is the study of data

True or False; Collecting and summarizing data may show abnormalities in the data that should be investigated further.

True: Summarizing data may point up features of the data that may call for further investigation and exploration.

continuous variables

Variables such as "time to respond to a question" are continuous variables since the scale is continuous and not made up of discrete steps. The response time could be 1.64 seconds, or it could be 1.64237123922121 seconds. Can be measured.

unrepresentative sample

aka a biased sample, is missing some or all of the characteristics found in the population from which it was selected.

cluster sample

includes some or all members of randomly selected clusters.

True or False; Inferential statistics is often the first step in statistical analysis of data.

False: The first step in statistical analysis of data is gathering and summarizing data, i.e., descriptive statistics.

Probability

A basic tool in the study and application of inferential statistics.

3. 75% more interracial marriages are occurring this year than 25 years ago. Thus, our society accepts interracial marriages. Would you accept this argument as proof that our society has become substantially more accepting of interracial marriages? What might be missing here?

A major flaw is that we don't have the information that we need. What is the rate at which marriages are occurring? Suppose only 1% of marriages 25 years ago were interracial and now 1.75% of marriages are interracial (1.75 is 75% higher than 1). But this latter number is hardly evidence suggesting the acceptability of interracial marriages. In addition, the statistic provided does not rule out the possibility that the number of interracial marriages has seen dramatic fluctuations over the years and this year is not the highest. Again, there is simply not enough information to understand fully the impact of the statistics.

Statistical Analysis

Statistical analysis is using the mathematics of probability and uncertainty to make inference about a population, based on a random sample from that population.

Inferential Statistics

The science of drawing conclusions about a population based on data collected from a sample.

Qualitative variables

are categories.

2. A study reported that the more churches in a city, the more crime there is. Thus, churches lead to crime. Do you agree that having more churches is likely to lead to increased crime? What is the flaw in the reasoning here?

A major flaw is that both increased churches and increased crime rates can be explained by larger populations. In bigger cities, there are both more churches and more crime. This problem, which will be presented in more detail in the lesson on correlational measures, refers to the third-variable problem. Namely, a third variable can cause both situations; however, people erroneously believe that there is a causal relationship between the two primary variables rather than recognize that a third variable can cause both.

1. A new advertisement for Ben and Jerry's ice cream introduced in late May resulted in a 30% increase in ice cream sales for the following three months. Thus, the advertisement was effective. What do you think might be a problem with the interpretation? Was the advertisement really effective? Why or why not?

A major flaw is that ice cream consumption generally increases in the months of June, July, and August regardless of advertisements. This effect is called a history effect and leads people to interpret outcomes as the result of one variable when another variable (in this case, one having to do with the passage of time) is actually responsible.

systematic sample

has a randomly selected starting point with every nth individual then selected. Systematic sampling is a type of sampling method in which individuals from a larger population are selected according to a random starting point and a fixed periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size. The main advantage of using systematic sampling over simple random sampling is its simplicity. It allows the researcher to add a degree of system or process into the random selection of subjects. Another advantage of systematic random sampling over simple random sampling is the assurance that the population will be evenly sampled. There exists a chance in simple random sampling that allows a clustered selection of subjects. This is systematically eliminated in systematic sampling. But can be biased since you could end up selecting more of one group over the others.

stratified sample

includes members of subgroups in proportion to their presence in the larger population.

Random assignment

involves the random division of a sample into two (or more) groups.

Datum

is a single value, often referred to as a score.

Population

is all the units of interest a researcher is interested in studying

Sample

is used in the actual study is a smaller group selected in such a way that it is representative of that population.

statistic

may be used as a best estimate of a parameter.

parameter

summarizes some numerical attribute of a population.

Parameter

A parameter is a (numerical) description of a population characteristic.

Population

A population, in statistics, is a discrete group of people, animals or things that can be identified by at least one common characteristic for the purposes of data collection and statistical analysis.

Sample

A sample is a part of a population selected in such a way as to be representative of the overall population.

Statistic

A statistic is a (numerical) description of a sample characteristic. In the broadest sense, "statistics" refers to a range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on data.

Inferential statistics -

Are used to make generalizations or predictions based on data that have been summarized. Typically, this involves obtaining data from a sample that has been selected from a larger population and using those data to make a generalization about that population. Inferential statistics are valuable when examination of each member of an entire population is not convenient or possible. For example, to measure the diameter of each thermometer probe that is manufactured in a facility is impractical, but you can measure the diameters of a representative random sample of probes. You can use the information from the sample to make generalizations about the diameters of all of the probes. Effective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination of the data. In this class, you may encounter what might seem like too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.The systems and techniques for making probability-based decisions and drawing conclusions about a population based on data collected from a representative sample.

Data Collection

Data collection is the systematic approach to gathering and measuring information from a variety of sources in order to answer questions, evaluate outcomes. and make predictions.

Interval scales

Interval scales are numerical scales in which intervals have the same interpretation throughout. As an example, consider the Fahrenheit scale of temperature. The difference between 30 degrees and 40 degrees represents the same temperature difference as the difference between 80 degrees and 90 degrees. This is because each 10-degree interval has the same physical meaning (in terms of the kinetic energy of molecules). Interval scales are not perfect, however. In particular, they do not have a true zero point even if one of the scaled values happens to carry the name "zero." Data on interval scales cannot be qualitative, as it is always quantitative.

Descriptive Statistics

Involves the organization, summarization and display of data.

Levels of Measurement

Levels of measurement build in complexity, from the most basic (nominal) to the most complex (ratio). Each higher level of measurement includes aspects of those before it. The following diagram visualizes these different levels of measurement.

simple random sample

SRS --is one in which every set of n individuals has an equal probability of being selected.

Data are the actual values of the variable.

They may be numbers or they may be words.

Variable

is a characteristic of interest for each person or thing in a population. Variables may be numerical or categorical. Numerical variables take on values with equal units such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. Values of the independent variable are levels. When a variable is manipulated by an experimenter, it is called an independent variable and the different experimental conditions are referred to as levels of the independent variable. The dependent variable "depends on" the independent variable.

statistic

summarizes some numerical attribute of a sample.

Ratio scales

The ratio scale of measurement is the most informative scale. It is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured. You can think of a ratio scale as the three earlier scales rolled up in one. Like a nominal scale, it provides a name or category for each object (the numbers serve as labels). Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers). Like an interval scale, the same difference at two places on the scale has the same meaning. And in addition, the same ratio at two places on the scale also carries the same meaning. Like interval data, the data on a ratio scale is also quantitative, the difference being the presence or absence of a true, or absolute, zero point.

Descriptive statistics -

The study of methods and tools for collecting data, and the organization, summarization and display of data. are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State, or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data. Descriptive statistics do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the job of inferential statistics.

True or False; Drawing a conclusion about a population based on data from a sample is an example of the use of inferential statistics.

True: Inferential statistics involves drawing conclusions based on samples of data.

Ordinal scales

Unlike nominal scales, ordinal scales imply an ordering of the responses, although the ordering does not imply that the intervals between the values, or responses, are equal. In this respect, ordinal scales fail to capture important information present in higher level scales, since the difference between two levels of an ordinal scale cannot be assumed to be the same as the difference between two other levels. Ordinal data can be described as either qualitative or quantitative.

discrete variables

Variables such as the number of children in a household are called discrete variables since the possible scores are discrete points on the scale. For example, a household could have three children or six children, but not 4.53 children. Can be counted.

Nominal scales

When measuring using a nominal scale, one simply names or categorizes responses. Gender, handedness, favorite color, and religion are examples of variables measured on a nominal scale. Numbers can also be used where the numbers only provide an identification of a category, like zip codes. The essential point about nominal scales is that they do not imply any ordering among the responses. Another way to look at it is that nominal data is qualitative rather than quantitative.

Quantitative variables

are either counted or measured. Some examples of quantitative variables are height, weight, and shoe size.

convenience sample

consists of participants that are easy to reach and readily available. There is no randomness or probability involved in the selection.

representative sample

contains all the characteristics and diversity found in the population from which it was selected.