Basic Statistics Data Used in everyday life

Introduction to Statistics: Data Collection and Data Concepts

Essential Information

Each week will include a Lesson that focuses on the Essential Information for that week. It is important to read this information for two reasons:

It will give you the skills, concepts, and material necessary to be successful in the homework, and
You will find a link to that week\’s Excel spreadsheet. Since this course focuses on the concepts and interpretation of statistics, these spreadsheets are designed to do the calculations for you. You will need the spreadsheets to complete the homework effectively and efficiently.
Note
Week 1 does not have an Excel spreadsheet because the Week 1 information is more definitional as we lay the groundwork for our statistics study.

Statistics

Statistics is largely a science of collecting, organizing, and interpreting data. From this definition, we get a good idea of what we will be learning in this class. In Chapters 1 and 2, we will learn about collecting data and how we can use data.

Statistics is an important tool for making a variety of health science decisions. For example, pharmaceutical companies will use data to see if their drug is improving health. For surgery decisions, statistics are shown based on proportions of successes or probable outcomes. Because statistics is used so often, it is important to understand the concepts when entering the health sciences.

Population Versus Sample

The very basis of statistics is to understand the difference between a population and a sample.

A population is the all, so to speak. If you are talking about all of the students taking an introductory statistics class, you have a large population. This could include students taking introductory statistics at Chamberlain University, at other universities in the states, at universities in other countries, and even some high schools. Usually, the population is a very large group.

Because of the size of a population, we may want to investigate a smaller subset of that population. This is our sample. A sample is a more manageable group that represents, or reflects, the population. For instance, if our population is all students taking an introductory statistics class, then our sample may be students at Chamberlain taking an introductory statistics class. While still a large group, it is a subset of the stated population. As a second example, if we considered all coronary angioplasty patients and studied 100 of them, the 100 would be our sample of the total population of angioplasty patients.

The differences between a sample and a population are important to distinguish. In some cases, different formulas are used if we are talking about a population or a sample. Further, sample data are used to make decisions about a population.

Performing a Statistical Study

Every statistical study is performed with the same basic steps.

State a goal. You will state what you are interested in studying, which will define the population of interest.
Take a sample. Typically, it would be too time consuming or costly to survey or test every member of your population, so you will need to decide how to create a manageable subset, or sample. You will decide the best sampling technique specific to this goal.
Collect your data. Now, you need to collect the data. You will also need to decide the best collection strategy, specific to this goal.
Make an inference about the population. This sample data will lead you to make a decision about your population. In statistics, we make our decisions about a population from our sample data.
Draw a conclusion. Did this sample answer the questions you wanted answered regarding your original goal? Sometimes, the answer here may be no. If not, then you may need to refine your goal and start all over.
Understanding the steps of a statistical study will make your task easier. If you do not plan well, then you may come to the end of your study without the correct data necessary to make the right decision. Putting the time and thought into the process from the beginning will lead to better results in the end.

Types of Statistical Studies

Observational: Observe or measure characteristics without influencing the results. An example would be watching children play to study their interactions.

Experimental: Study the effects of a treatment. An experiment could be used to study a new cold medicine. People with colds would be divided into two groups: one that take a new medicine and one group that takes a placebo. The results from the two groups are then compared using statistics to see if the new medicine is effective.

Design of Experiments

Three types of good design methods for experiments include replication, blinding, and randomization.

Replication is an experiment that is repeated on more than one individual. Sample sizes must be large enough to show marked effects of treatments.
Blinding is an experiment in which the subject does not know if he/she is receiving a treatment or a placebo (a harmless pill or medicine). Blinding is a way to guard against the placebo effect, which occurs when an untreated person believes there are improvements, either real or imagined, in his/her symptoms.
Randomization occurs when individual subjects are assigment to different groups through a random selection process.
Sampling Techniques

There are several basic sampling techniques that you could use. Choosing the correct technique will depend on your goal.

Systematic sampling—Systematic sampling will choose every nth member. A good example of a systematic sample is patient satisfaction interviews. If a quality assurance program wants to gain personal insights into patient satisfaction, then it could systematically pick every 25th patient discharged to make sure that a range of patient characteristics are included in the study.
Convenience sampling—A convenient sample is created just that way—conveniently. If you are interested in finding out the predominant eye color of coffee drinkers, then where is the best place to find coffee drinkers? You may stand outside of a Starbucks and survey everyone\’s eye colors. It is convenient to find coffee drinkers at a Starbucks.
Cluster sampling—A cluster sample creates clusters from a population, randomly selects some of those clusters, and then include all the people or things within the selected clusters as the sample. For example, if you are interested in determining the average income per household within your state, you may use each of the counties of the state as a cluster. If you randomly select two or three of those counties and survey the households\’ incomes in those selected counties, you would have a cluster sampling of your state.
Stratified sampling—A stratified sample is a defined subgroup of the population. A stratified sample would include a similar percentage in the sample as represented in the populations. A familiar example of a stratified sample would be from a hospital unit. If you are interested in seeing if a particular unit has more satisfaction among the staff, then the strata from your population would be unit level. If the hospital has 3,000 staff consisting of 30% in surgery, 28% in neonatal, 25% cardiac, and 17% pediatric, you would create a sample with the same percentage of levels. Your sample may have only 100 staff, but you would want the strata to have the same percentage of units represented.
Data, Data, Data

As we know already, we need data.

Classifying Data

Data are defined in several different ways. First, you need to decide what type of data you have; then, you can decide what level of data you have.

Type of data

Qualitative—Data placed in nonnumerical categories

QuaLitative data—\’L\’ is for letters, or nonnumeric

Quantitative—Numeric data

QuaNtitative data—\’N\’ is for numbers

Another type of classification is between discrete and continuous

Discrete—A whole number, like how many students in class would be a discrete number

Continuous—A number that can take on any value. To distinguish, ask yourself if a decimal place makes sense. An example would be students\’ heights.

Discrete vs. Continuous Classification

Can you have a fraction of a Liter of solution in your patient? Which classification is it?

View Answer
Yes, you can put a fraction of a Liter of solution into your patient. This classification is an example of continuous.

Can you have a fraction of a cat? Which classification is it?

View Answer
No, it doesn\’t make sense to divide up a cat, so, this classification is discrete or an example of a whole number.

Level of measurements (from lowest to highest)

Nominal: Qualitative data—No mathematical application
Names, labels, or categories
Examples: Numbers on a football jersey, models of cars, gender

Ordinal: Qualitative data with order—No mathematical application
Qualitative data that is ranked
Examples: First, second, third place; freshman, sophomore, junior, senior

Interval: Quantitative—Arbitrary zero
Arbitrary zero does not mean nothing.
Examples: Temperature (in Fahrenheit or Celsius) and year
If the temperature outside is zero, does that mean there is no temperature? No, it is just the designated zero in that temperature system.

Ratio: Quantitative—Zero means nothing
All numbers that are used in mathematical operations
Example: If a salesman made zero sales for the month, he sold nothing. Zero literally means nothing.

Bias in a Statistical Study

Collecting the right data is very important for the integrity of a research study. If the data does not represent the intended population, you will create a bias in your results. A biased sample will bring questions to the effectiveness of the research.

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Bias can come in several forms:

Selection Bias: Selecting a sample in a biased way. For example, instead of creating a stratified sample by units, only administrators were surveyed regarding all staff satisfaction. As administrators may have a different experience than much of the staff, the data are biased based on the sampling.
Participation Bias: Voluntary participation. For example, if patient satisfaction surveys are voluntary, the outcome may be biased and not truly reflect the satisfaction of most patients.
For each of the sampling techniques, try to think of examples that would create bias within the study.
Percentages and Indices
Percentages are all around from the 25% discount at the store to a 3% pay increase. There is a basic structure to finding percentages: (ending – beginning) ÷ beginning

So, if a prescription initially cost $50 and was discounted to $40, you could use this formula to find the percentage of the discount. This is an absolute change of $10. The relative change is the same as the percentage change. In this example, the beginning price is 50 and the ending price is 40. Notice that beginning and ending are based on time frame, rather than which is smaller or bigger. The price used to be $50 and is now $40, so it started at $50 and ended at $40.

(40 – 50) ÷ 50 = -10 ÷ 50 = -1 ÷ 5, or -20%

So, there was a 20% discount on the original price. The negative in front of the percentage indicates the value decreased, or went down, from the beginning point to the ending point.

Indices are calculated using percentage changes. Examples of indices are the Consumer Price Index for inflation or the cardiac index for heart performance. An index has a starting point, usually set to 100. Then, the other numbers in the index are stated relative to that staring point. Let\’s say that you want to compare the height of a tree from the time you moved to your home. If you moved in during 2005 and the tree was 4 feet tall, then a height of 4 feet would be set to an index value of 100. Here is a table of tree heights

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Year Height of Tree Index
1995 3 ft
2000 3.8 ft
2005 4 ft 100
2010 4.6 ft
2015 6.1 ft
To find the index value in other years, take the value in the year of interest and divide it by the starting point value and multiply the result by 100. To find the index for 1995, the value in that year was 3 ft and you divide that by the starting point value of 4 ft and then multiply by 100:

3 ÷ 4 × 100 = 75

So, the index value in 1995 was 75. This same process can be used for the other years in the table.

Year Height of Tree Index
1995 3 ft 75
2000 3.8 ft 95
2005 4 ft 100
2010 6.6 ft 165
2015 8.2 ft 205
You can tell from looking at the index that the tree is about twice as tall as it was when you moved in.

SAMPLE SOLUTION

Initial post
Two of the main types of data I frequently use in the field are pulse oximetry and temperature. I use pulse oximetry to check patients on how well their hearts pump blood and supply oxygen throughout the body, especially individuals diagnosed with chronic obstructive pulmonary disease (COPD). On the other hand, I use temperature measurements to establish its relationship with the COPD | PLACE YOUR ORDER NOW AT writtask.com | is quantitative because it gives quantitative values indicating a patient’s degree of the internal heat | PLACE YOUR ORDER NOW AT writtask.com | gives both quantitative and qualitative data. Qualitative data results from sounds produced by the pulse oximeter corresponding to the oxygen saturation levels while quantitative data results from the display of a pulsatile waveform corresponding to the arterial | PLACE YOUR ORDER NOW AT writtask.com | and temperature are both interval scales. The interval scale is one where attributes constituting variables are measured on specific numerical values or scores and the distances between attributes are equal (Priyadarshan, 2019)…