# Final Review This includes notes taken for chapters 1-11... minus chapter 12 and the other really basic straightforward ones.

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Published on 16 Oct 2011

Department

Kinesiology & Health Science

Course

KINE 2050

Professor

o CHAPTER 1 – INTRODUCTION

1.1 Why Learn Statistics?

What does science consist of and what are the main operations that scientists perform in all disciplines? The

answer is Observation.

o The essential event in any observation is being able to accurately gather measurements which result in

sets of numerical data. Scientists observe in order to understand the relations between events and also to

discover the laws that govern natural phenomena

o Statistics is a methodology for extracting information and making meaning out of numbers and then being

able to make decisions about the numbers and information. It is the intermediary between what is

observed and what can be concluded about how natural events operate

1.2 What Is Statistics?

We use statistical methods for two main purposes: (1) Description and (2) Inference

(1) Descriptive Statistics: This consists of techniques for organizing, summarizing and extracting

information from gathered numerical data. Usually this is found in graphical form. Descriptive procedures are

quite basic to understanding data and constitute the first stage of analysis

(2) Inferential Statistics: This involves generalizing the findings beyond the immediate observations.

Inferential statistics is the body of rules and procedures by which general statements are made about people

or events based on the observation of a relative few.

*Overall, Statistics may be defined as the body of rules and procedures for evaluating and making decisions

about the outcome of scientific observation.

1.3 How To Learn Statistics

The point of Statistics is to make decisions and not to manipulate number as an end in itself

1.4 Calculators & Computers

o Statistics programs fall into 2 categories: (1) Dedicated Statistical Applications (There are many dedicated

statistical applications such as SAS, SPSS and INSTAT) and (2) Spreadsheets (Microsoft Excel).

CHAPTER 2 – DATA: Review Exercises

2.2 Review Exercises

1. Define or describe the following terms:

(a) Population: A population consists of all the organisms, objects, or events of a specified type. Population

membership must be clearly defined so that it can be clear who and who is not included in that population.

(b) Sample: A sample is any subgroup or subset of a population. Usually populations are so large that it is

impractical to observe all the members of the population so scientists often randomly chose members of the

population that represent the population and this is termed a „sample‟.

(c) Parameter: A parameter is a numerical term that summarizes or describes a population.

(d) Statistic: A statistic is a numerical term that summarizes or describes a sample.

(e) Datum: Any particular observation such as an individual‟s height is termed „datum‟. It is the singular form of data.

(f) Raw Data: Observations that are recorded and gathered together. These observations and measures have NOT

been manipulated in any way.

(g) Variable: A variable is any observable/measurable characteristic of organisms, objects, or events such that

individuals may differ in amount or kind of this property.

(h) Quantitative Variable: A quantitative variable is a variable in which the number obtained from the measurement

reflects the amount of the property in question. (ex. Length, height and weight)

(i) Qualitative Variable: A qualitative variable is a distinction of kind and NOT amount. (ex. Male or Female and

Hair Colour)

(j) Continuous Variable: A continuous variable is one that may assume any value between maximum and minimum

limits. With a continuous variable, the value can become more and more precise. (ex. Height; saying you are 5‟3 is

more precise than you simply stating that you are 5 feet tall)

(k) Discrete Variable: A discrete variable is one that can only assume certain numerical values. (ex. How many

siblings you have. You cannot have 2.3 siblings, it must be a whole number)

2. Identify the following variables or measures as being either quantitative or qualitative

(a) Colour of Barbara‟s eyes: Qualitative

(b) Heart Rate: Quantitative

(c) Catholic: Qualitative

(d) Reaction Time: Quantitative

(e) Pupil Dilation: Both?

(f) Hungarian: Qualitative

(g) Crop Yield: Quantitative

(h )Paranoid Schizophrenic: Qualitative

3. Identify the following variables or measures as being either continuous or discrete

(a) Body Temperature: Continuous

(b) Atmospheric Pressure: Continuous

(c) Income Tax Bracket: Discrete (not completely sure)

(d) Sales Resistance: Continuous

(e) Number of books in the library: Discrete

(f) Amount of money in your pocket: Discrete

(g) Lung Capacity: Continuous

2.3 Review Exercises

1. Define or describe the following terms:

(a) Objective: An objective observation is one that is not in any way affected by the opinions, values, or biases of the

observer. (ex. When you go home you tell your parents that your statistics professor has a mustache. This is

objective because anyone who was there would report the same thing)

(b) Subjective: A subjective observation is one that reflects the observer‟s personal point of view; clearly there can

be no science if the raw data are based on opinion. (ex. You believe your statistics professor is hard, but hard

depends on your views of what is hard. This will change depending on each and every persons views of difficulty)

(c) Empirical Event: An empirical event is one which may be perceived by our senses (including any extension of

them in form of detection and/or recording device). Science is an empirical enterprise because it deals with

observable events and because its findings are based on objective observations rather than subjective ones.

(d) Operational Definition: An operational definition of a variable specifics the manner of measurement of the

variable. There are essential in science because they are a means by which we can achieve precision in our

communication and objectivity of our data. (ex. Speed can be described as fast or slow but that would be subjective.

By defining a speed by km/hr or m/hr there would be no misunderstanding about how speed was measured and the

value would not change depending on who is making the measurements)

2. Which of the following are operational definitions?

(a) Popularity: No

(b) Number of times Brenda is asked to dance: Yes

(c) Anxiety: No

(d) Height: Yes

(e) Score on LQ Test: Yes

(f) Degree of addiction to caffeine: No

(g) Mark on an exam: Yes

(h ) Intelligence: No

(i) Number of cups of coffee consumed per day: Yes

(j) Number of seconds devoted to an item on the evening news: Yes

(k) Amount of money earned by a racehorse during a season: Yes

(l) An alcohol content in the blood of 0.8 percent or greater: Yes

2.6 Review Exercises

1. Define or describe the following terms:

(a) Ratio Measurement: Ratio measurement is quantitative; this means the numerical values are assigned in such a

way that the size of the number reflects the amount of the variable being measured. A ratio measure HAS a true zero

point, which means that a value of 0 reflects an absence of the variable in question. In ratio measures, the numbers

bear both a consistent interval relationship (distance b/w 2 values is always the same) and ratio relationship to each

other (ex. 2cm is the same as 1cm x 2). Ratio measurements CANNOT yield negative scores (ex. Time is seconds,

weight in pounds, number of correct answers on test)

(b) Interval Measurement: Interval measurement is quantitative, meaning that it yields numbers that reflect the

amount of the variable. Unlike ratio measurement, an interval measure does NOT have a true zero point. This means

that in an interval measure, the zero value is defined arbitrarily and does not reflect an absence of the variable. (ex.

When it is 0 degrees Celsius outside it does not mean that is no cold or no temperature).In internal measurement, the

numerical values bear a consistent interval relationship to each other. Internal Measurement CAN yield negative

scores (ex. -15 degrees Celsius).

(c) Ordinal Measurement: Ordinal measurement consists of rank ordering (ex. 1st runner up, 2nd runner up, 3rd,

etc.). Ordinal measurement is NOT quantitative and the numbers assigned reflect only the ordinal position (rank) and

do NOT in any way measure or reflect the amount or magnitude of the variable.

(d) Nominal Measurement: Nominal measurement is classification. In nominal measurement the individuals or

objects are classified as belonging to one or another of a set of categories (ex. Male or female or Hair Colour

Groups). Nominal measurement requires a set of categories which is exhaustive, meaning that the range of

categories is sufficient enough to include everyone being observed. The categories mush be mutually exclusive,

meaning that any individual can only belong to one category (ex. If you are male you cannot be female).

2. What type of measurement is occurring in each case?

(a) Kilometers per hour: Ratio Measurement

(b) 5th ranked heavyweight: Ordinal Measurement

(c) “Ladies & Gentlemen”: Nominal Measurement

(d) Exam Grades (A.B, C, etc.): Nominal Measurement

(e) Outcome of a coin flip: Nominal Measurement

(f) Amount of money in your bank account: Ratio measurement

(g) Day of the week: Nominal Measurement

(h )Income Tax Bracket: Ratio Measurement (Not sure)

(i) Degrees Kelvin: Ratio measurement

(j) Top seed in a tennis tournament: Ordinal Measurement

(k) Exam Marks: Ratio or Interval Measurement? Depends on if it measures in % (interval) or in marks (ratio)

(l) Percentage of people absent from class today: Ratio Measurement

(m) Qualifying position in pre-race time trials: Nominal Measurement (Not sure)

*** Chapter 3 - Some Descriptive Statistics

3.3 Review Exercises

CHAPTER 3 – SOME DESCRIPTIVE STATISTICS

3.3 Review Exercises

1. Define or describe the following terms:

## Document Summary

The answer is observation: the essential event in any observation is being able to accurately gather measurements which result in sets of numerical data. It is the intermediary between what is observed and what can be concluded about how natural events operate. We use statistical methods for two main purposes: (1) description and (2) inference (1) descriptive statistics: this consists of techniques for organizing, summarizing and extracting information from gathered numerical data. Descriptive procedures are quite basic to understanding data and constitute the first stage of analysis (2) inferential statistics: this involves generalizing the findings beyond the immediate observations. Inferential statistics is the body of rules and procedures by which general statements are made about people or events based on the observation of a relative few. *overall, statistics may be defined as the body of rules and procedures for evaluating and making decisions about the outcome of scientific observation.