NUR 80A/B Lecture Notes - Lecture 7: Statistical Inference, Statistical Parameter, Sampling Frame
14 Mar 2020
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⚫ Probability
⚫ The Normal Curve
⚫ Z scores
⚫ Sampling Distributions
⚫ Sampling Error
⚫ Standard Error of the Mean
⚫ REQUIRED READINGS / MATERIALS
⚫ Woo (2019), Chapter 14, pp. 245-246
⚫ Salkind (2017), Chapter 8
⚫ Why probability?
⚫ Is the basis for the normal curve and is the foundation for inferential statistics
⚫ We estimate population parameters from sample statistics
⚫ Allows researchers to draw conclusions (inferences) about a population based on data
from a specific sample
⚫ Therefore, probability establishes a connection between samples and populations
⚫ How probability works
⚫ Researchers collect data from one sample
⚫ ideally representative of the population (probability sample)
⚫ Researchers must decide whether sample values (statistics) are good estimate of
population parameters
⚫ i.e. mean knowledge scores
⚫ Inferential statistics are used to help the researcher determine the mathematical
probability that the findings reflect the actual population parameter versus being due to
chance alone
⚫ For example …
⚫ A researcher is interested in knowing the level of knowledge that nursing students have
in statistics (before they take the research course!!)
⚫ The researcher randomly selects 25 nursing students from a population of 500 in a
nursing program (Sampling frame) and asks them to complete a statistical knowledge
test
⚫ The mean score on the test is 75% and the SD = 5
⚫ The researcher must then determine the likelihood (probability) that this mean reflects
the actual level of knowledge within the population of nursing students.
⚫ Probability (cont’d)
⚫ Laws of probability allow estimation of how probable an outcome is
⚫ Probability helps to evaluate the accuracy of a statistic and to test hypotheses
⚫ Probability helps us increase our confidence that a finding is “true” (did not likely
happen by chance)
⚫ All probabilities range between 0% & 100%
⚫ Probability (cont’d)
⚫ Probability of outcome =
number of outcomes
total number of possible outcomes
⚫ Probability and frequency distributions
⚫ As you know, samples and populations can be presented as frequency distributions
using frequency polygons
⚫ The area under the curve of a frequency polygon represents 100% of all cases
⚫ Sections of the area under the curve represent proportions of all cases
⚫ Those proportions provide us with probabilities
⚫ A normal curve divided into different sections
⚫ Distribution of cases under the normal curve
⚫ Why study the normal curve?
⚫ Provides the basis for:
⚫ understanding probability associated with any outcome
⚫ having confidence that the findings from a study are ‘true’ and not obtained by
chance
⚫ Probability and the
normal distribution
⚫ The normal distribution is a probability distribution!
⚫ What are the characteristics of the normal distribution?
⚫ __symmetrical in shape___
⚫ __mean=median and mode are approx. equal___
⚫ ___tails asymptotic__
⚫ Events or scores that fall in the middle are more likely to occur than those that fall in the
tails.
⚫ The Normal Curve
(aka: bell-shaped curve)
⚫ How scores can be distributed
⚫ In general, many events occur right in the middle of a distribution with few on each end
⚫ SD and normal distributions
⚫ When we plot a frequency polygon of a set of scores, the area under the curve
represents all of the scores
⚫ If the distribution of scores is approx. normal, we can determine where a certain
percent of cases is going to fall
⚫ We do this using the standard deviation ( how much a scores are dispersed from the
mean)
⚫ In a normal distribution, a fixed percent of cases fall within certain distances from the
mean
⚫ So…going back to the slide titled “Distribution of cases under the normal curve”, what
can we say about:
⚫ 68% of scores? __within -1 to +1 SD___
⚫ 95% of scores? __within -2 to +2 SD__
⚫ 99% of scores? __within -3 to +3 SD___
⚫ SD and normal distributions
In any normal distribution we know that:
⚫ 34.13% of scores fall 1SD above the mean
⚫ 34.13% of scores fall 1SD below the mean
⚫ 13.59% of scores fall between 1 and 2 SD above the mean
Document Summary
Is the basis for the normal curve and is the foundation for inferential statistics. We estimate population parameters from sample statistics. Allows researchers to draw conclusions (inferences) about a population based on data from a specific sample. Therefore, probability establishes a connection between samples and populations. Ideally representative of the population (probability sample) Researchers must decide whether sample values (statistics) are good estimate of population parameters. Inferential statistics are used to help the researcher determine the mathematical probability that the findings reflect the actual population parameter versus being due to chance alone. A researcher is interested in knowing the level of knowledge that nursing students have in statistics (before they take the research course!!) The researcher randomly selects 25 nursing students from a population of 500 in a nursing program (sampling frame) and asks them to complete a statistical knowledge test. The mean score on the test is 75% and the sd = 5.
