Data Analysis

Descriptive and Inferential StatisticsApril 11, 2013

Importance of Statistics in Nursing Research

Researchers link the statistical analyses they choose with the research question, design, and level of data collected.

Allows us to critically analyze the results.

Provide organization and meaning to data.

Where Do You Find Them?

Methods section will contain the planned statistical analysis.

Results section will provide the data generated from testing the hypothesis or research questions.

Data is the analysis using descriptive and inferential statistics.

Levels of Measurement

Measurement is the process of assigning numbers to variables.

For example: Males and females in a study.Males would be assigned as 1 and females assigned as 2.

Every variable in research study that is assigned a specific number must be similar to every other variable assigned that number.

Levels of Measurement

Nominal- aka categorical, naming or classifying. Either does or does not have the characteristic.

Lowest level of measurement and allows for the least amount of statistical information.

Examples- gender, marital status, religious affiliation.

Can you think of one?

Ordinal

Used to show relative rankings of variables or events. Ranks in order from high to low, but does not

indicate how much higher or how much lower. Intervals are not necessarily equal and there is no

absolute zero. Limited in the amount of mathematical manipulation

possible. Examples- class rank, levels of wellness, levels of

height.

Interval

Shows rankings of events or variables on a scale with equal intervals between.

Zero point remains arbitrary and not absolute.Allows for more mathematical manipulation of

data.Examples- test scores and temperature on a

Fahrenheit scale.

Ratio

Shows rankings of events or variables on scales with equal interval and absolute zero.

Most often used in physical sciences.Highest level of measurement, allows for most

manipulation of data.Number represents the actual amount of the

property the object possesses.Example- height, weight, pulse and BP.

NOIR

NoOilIn Rivers

Descriptive Statistics

Procedures that allow researchers to describe and summarize data you definitely know (describes the sample).

Examples: Demographics, clinical data.

Frequency distribution is one way to display data. See page 313.

http://youtu.be/ZSGy1jfB1jA

Descriptive Statistics

Measures of central tendency are used to describe the pattern of responses among a sample.Mean- most frequently used average, add up

numbers (sum) and then divide by the #. Defined as a balance point in a distribution of scores.

Median-50% are above and 50% are below the score. Defined as the middle point in a distribution. Insensitive to extreme scores.

Mode-Most frequently occurring score. May have more than one mode.

Normal Distribution

Most important curve (Bell-shaped).

Most often found in nature and used as the basis for a number of inferential statistics.

Mean, median and mode are equal.

Measure of Variability

Concerned with the spread of data. Range- the difference between the highest and lowest

score. Semiinterquartile range- indicates the range of the

middle 50% of the scores. Standard Deviation-most stable and most useful,

provides an overall measurement of how much participants scores differ from the mean of the group.

Z score-used to compare different measurements, scores are converted to Z scores and them compared.

Inferential Statistics

Data collection procedures that allow researchers to estimate how reliably they can make predictions and generalize findings.

Allows us to compare groups and test hypothesis.

Answer research question in a study.http://youtu.be/lgs7d5saFFc

Inferential Statistics

Parameter- a characteristic of a population.

Statistic- characteristic of a sample.

Not possible to study the whole population so we study a sample and make predictions or statements related to our findings.

Inferential Statistics

2 important qualifications must be conducted to use inferential statistics.

Sample must be representative (drawn with probability, some form of random selection).

Scale used must be either interval or ratio level of measurement.

If nonprobability sampling occurs techniques such as power analysis are used to compensate for this.

Inferential Statistics

Researchers are able to make objective decisions about the outcome of their study by using statistical hypothesis testing.

Scientific hypothesis is what the researcher believes will be the outcome of the study.

Null hypothesis is what can actually be tested by the statistical methods.

Inferential stats use the null hypothesis to test the validity of a scientific hypothesis.

Inferential Statistics

Probability- the notion that in a repeated trial/study under the same conditions we would get the same results.

Statistical probability is based on sampling error. The tendency for stastics to fluctuate from one sample to another is known as sampling error.

Type I and Type II Errors 2 types of errors in statistical inference. Type I- researcher rejects a null hypothesis when it is actually

true. Type II- researcher accepts a null hypothesis that is actually

false. Type I errors are considered more serious because if a

researcher declares that differences exist when none are present the potential exists for patient care to be adversely affected.

Type II errors occur when sample is too small.

Level of Significance

The probability of making a type I error.

Minimum accepted level for nursing research is 0.05.

“ If I conduct this study 100 times, the decision to reject the null hypothesis would be wrong 5 times out of 100”

LOS

If wanting to assume smaller risk level will be set at 0.01.

Meaning researcher is willing to be wrong only once in 100 trials.

Decision to use alpha level 0.05 or 0.01 depends of the study significance.

Decreasing the risk of making a type I error increases the risk of making a type II error.

Parametric and Nonparametric Statistics are used to determine significance.

Parametric have 3 attributes:1. Estimation of at least one population parameter.2. Require measurement on at least an interval scale.3. Involve certain assumptions about the variables being

studied. Variable is normally distributed in the overall

population. Most researchers prefer parametric statistic when

possible because they are more powerful and more flexible.

Nonparametric

Not based on the estimation of population parameters; usually applied when variable measured on a nominal or ordinal scale , or distribution of scores is severely skewed.

Table 14.3 and Table 14.4, page 324. Most commonly used inferential statistics.

Most Commonly Used Inferential Statistics

Parametric t statistic-commonly

used in nursing research, tests whether 2 group means are different.

ANOVA ANCOVA

Nonparametric Chi-square- used when

data is at the nominal level, determine difference between groups. Robust and used with small samples.

Fisher’s exact probability.

Tests of Relationships

Interested in exploring the relationship between 2 or more variables.

Studies would use statistics to determine the correlation or degree of association between 2 or more variables.

Pearson r, the sign test, the Wilcoxon matched pairs, signed rank test and multiple regression.

Review Questions

1. Statistics are used in nursing research to :a. Help us organize and understand the data

generated.b. Help us to publish our study results.c. Help us to analyze data that can be useful in

practice.d. Help us to determine if results have practical

value.

2. List the four levels of measurement:

• ___________________• ___________________• ___________________• ___________________

3. The level of measurement that allows for the most manipulation of data and is used most often in the physical sciences is?__________________4. Give 2 examples of this level of measurement:• _____________• _____________

5. Define descriptive statistics.

6. Define inferential statistics.

7.List the measures of central tendency.• ______________• ______________• ______________

8. The bell shaped curve is:a. Used often in inferential statistics.b. Known for the mean, median and mode

being equal.c. Found most often in nature.d. All of the abovee. A & B.

9. Type ____ errors are most serious because they can negatively impact patient care.

10. Rejecting the null hypothesis when it is true is what type error?

Extra Credit

11. What is the lowest level of measurement and why?