Before going into the details about statistics it’s important to clarify some concepts:

Critical Thinking: Critical thinking is the set of skills that allow you to understand and asses the limitations of statistical methods. That way you're aware of the assumptions, appropriateness, biases, and justifiable conclusions.

Statistical Literacy: As with any science, yo’re expected to master the statistical jargon, including its concepts and methods.

Why Statistics: Page 02 Some problems are way too costly and complex to be analyzed using traditional mathematical methods; so, we are forced to make educated guesses on limited information. For this kind of situations statistical methods are an excellent tool. However, statistics are not a replacement for a in-dept. knowledge of the field where it is being applied. Statistical Methods are not a miracle cure.

What is Statistics: Is the study of how to (a) Collect (b) Organize (c) Analyze and (d) Interpret , numerical information from data.

Population: Consist of all individuals of the set.

Sample: A portion of all the individuals of the set.

Random Sample: A sample consisting of 𝑛 number of individuals from a population, chosen without using any type of pattern.

Individuals: People or objects included in the study

Variable: A characteristic of the individual to be measured or observed in the study. The characteristic can be Quantitative or Qualitative.

Random Variable: Characteristinc measured in an experiment that, by chance, can get different values.

Quantitative Variables: Have numerical measurement

Qualitative Variables: Place the individual in groups |categories. Sometimes called Categorical Variables. Is non-numerical, collected by visual observation.

Parameter: Numerical measure that describes an aspect of the population.

Statistic: Numerical measure that describes an aspect of a sample. Statistics estimates parameters.

Random samples are the best samples we can take to make inferences about the population. However, the inferences have a degree of uncertainty, but the uncertainty is measurable using probability.

Levels of Measurement: 1. Nominal (b) Ordinal (c) Interval (d) Ratio

Nominal: Means “in name only”. Not intended for numerical calculation, but to be placed in categories. For looking at it you can’t determine any ordering of the individuals that would be meaningful. e.g. (1) Taos, Acoma, and Cohiti are the names of Native American Pueblos.

Ordinal: Nominal, plus, data can be arranged in order, smallest to larger, worst to best; but the differences are meaningless. e.g. (1) stars rating give you an idea of how good or bad something is relative to other, but it tells nothing about how much. 4 stars rating is not necessarily twice better as 2 stars. (2) Rankings in a cla, based on GPA, tells you what comes first but gives you no idea of the difference between them. On raking students, for example, the difference between 1st and 2nd could be as low as 0.01, or as large as 1 full point, or larger.

Interval Level: Ordinal, plus, differences between individuals are quantified, and meaningful. However, there is no zero starting point, so, we can’t stablish ratios. e.g. (1) 30 °C is 15° larger than 15 °C, but it doesn’t means it is twice as hot, because 0° Celsius is not an absolute zero. Zero Celsius doesn’t means zero heat.

Ratio: Interval, plus, includes a zero starting point, so, we can take ratios between individuals. e.g. (1) We can say that 𝑦° Kelvin is twice as hot as 𝑥° Kelvin. (2) Money: we can say that $20 is twice as much money as $10.

Exercises: pages 5, 6, 7, 8

Critical Thinking: 1. Specify the process and requirements for

measurement for any variable to measure.

2. Be sure your instrument really measure what you intent. e.g. If you want to know people knowledge and ask them where a place is located they could lie, affecting results. It would be more effective to ask them to show the place in a map.

3. Are you working with a sample , or a population…