OPST 196: Module 3: Understanding the concepts of probability and the normal curve (copy)

normal distribution

first graph = On this graph the concentration, mostly those that take part in the test, their scores fall at the range of 70-95. On the ends, are the smaller number of people. It is called the ________.

Symmetrical and bell-shaped

CHARAC OF NORMAL DISTRIBUTION: What you have on the left portion of data points are actually the same with the proportion that we have on the right.

Max height at mean

CHARAC OF NORMAL DISTRIBUTION: Point where you have most of your participants at a greater number.

Steady increase of decrease from the mean

CHARAC OF NORMAL DISTRIBUTION: Median point is Zero (0).

X is continuous

CHARAC OF NORMAL DISTRIBUTION: Your data is not just domino or binary., You have a ____ value for your X which you can quantitatively or numerically represent on your X axis. All these numbers at the bottom are actually meaningful numbers.

Most scores fall within 3 standard deviations from the mean

CHARAC OF NORMAL DISTRIBUTION: From the left to the right point, it captures most of your data points.

normal curve

We can also describe the proportions of your data points from your sample using the ____ ____.

mean

x̅ represents the

standard deviation.

SD signifies

68%

1 SD what percent

95%

2 SD what percent

99.7%

3 SD what percent

how many data points would actually correspond to the majority

With the normal curve, assuming that you have data that represents the normal curve, that means that you can actually approximate _____, say for instance relative to the mean. You can describe it since the data that you have is uniform and symmetrical.

3SDs

Most scores fall within the ___ of the mean: If you have that normal distribution

X̄ +/- SD

formula to find endpoints of the normal curve

Standardized scores (z-scores)

Directly indicate how many standard deviations they are from the mean, Easier reference, ____ the distributions that you have using specific numbers; _____ distributions = change x axis with 0 at mean and sd of 1

x - u/ o

formula of z in population

x = x bar / s

formula of z in sample

z-score table

We can also determine the proportion of our sample that represents a score above or below it. This is where you will be using

“area between 0 and z” / “area above z”

numbers to be used to compute for the proportions under the normal curve

positively skewed, right skewed, skewed to the right

WHAT IF THE DISTRIBUTION IS NOT NORMAL? Data set concentrated on the left:

negatively skewed, left skewed, skewed to the left

WHAT IF THE DISTRIBUTION IS NOT NORMAL? Data set concentrated on the right:

Skewness

Measure of the asymmetry of the distribution , Data set concentrated on the right: negatively skewed, refer where the line is thinning

Kurtosis

OTHER DISTRIBUTION MEASURES: Measure of the “tailedness” of the distribution

platykurtic

negative kurtosis:

leptokurtic

positive kurtosis:

mesokurtic

normal distribution:

Probability

Quantitative measure of the likelihood of an event; Chance, likelihood, certainty

0 to 1

probability Numeric values range from

0

= an outcome cannot occur

1

= an outcome will certainly occur

number of favorable outcomes/number of possible outcomes

probability formula

Normal distribution

There are different models of probability, and the best model to use depends on the data distribution we have; The ___ ___ is one example of the probability models that scholars use____ ___ is common but not all data points would give you a ___ ____ set

predictive

Probability is ____ as it applies to what we can expect a given outcome to occur in the “idealized” long run

make inferences about population parameters

Our goal: _______: We need to understand how a sample functions within a population

SAMPLING ERROR

Tendency for sample values to differ from population values; Will the mean and standard deviation be the same from these two groups? There will always be differences, no matter how many times we take the sample means

population means

SAMPLING DISTRIBUTION OF THE MEANS: Most of the sample means would be close to the

normal

SAMPLING DISTRIBUTION OF THE MEANS: would have ___ distribution

Standard error of the mean

The standard deviation of a theoretical sampling distribution of means; indicator of the degree of sampling error

SE = s/ sqrt n

Measure of variability

increases

As sample size ____, samples become more representative of the population;

smaller

As sample size increases hence, the sampling error becomes ___

decreases

Square root of n increases = Standard error ___

larger

in quantitative work, if you have ___ samples, the better and the higher the tendencies to see the effects that you’re looking at

Raw scores → z-scores → areas under the normal curve

With the mean and standard deviation from one sample, the probabilities associated with any range of values can be determined

TRue

T/F" Given a population mean and a standard error of the mean, the probabilities associated with any range of sample means can be computed

z = M-uM / oM

formula of population sampling distribution of the mean