SOC212 - Application Question #2

candi26oc

chapter_8_power_point.pptx

Home >Social Science homework help >SOC212 - Application Question #2

How probability relates to statistics

Characteristics of the normal curve

(i.e., bell-shaped)

How to compute z scores

How to interpret z scores

How to interpret the area under the normal curve

What You Will Learn in Chapter 8

Basis for the normal curve

Provides basis for understanding probability of a possible outcome

Basis for determining the degree of confidence that an outcome is “true”

Example: Are changes in student scores due to a particular intervention that took place or by chance alone?

Why Probability?

Visual representation of a distribution of scores

Three characteristics…

Mean, median, and mode are equal to one another

Perfectly symmetrical about the mean

Tails are asymptotic (get closer to horizontal axis but never touch)

The Normal Curve (a.k.a. The Bell Curve)

The Normal Curve

In general, many events occur in the middle of a distribution with a few on each end.

Hey, That’s Not Normal

For all normal distributions…

Almost 100% of scores will fit between –3 and +3 standard deviations from the mean

So…distributions can be compared

Between different points on the x-axis, a certain percentage of cases will occur

More Normal Curve 101

What’s Under the Curve?

The distance between…	Contains…	And the scores that are included (if the mean = 100 and the standard deviation = 10) are…
The mean and +1 standard deviation	34.13% of all the cases under the curve	From 100 to 110
+1 and +2 standard deviations	13.59% of all the cases under the curve	From 110 to 120
+2 and +3 standard deviations	2.15% of all the cases under the curve	From 120 to 130
+3 standard deviations and above	0.13% of all the cases under the curve	Above 130

What’s Under the Curve?

The distance between…	Contains…	And the scores that are included (if the mean = 100 and the standard deviation = 10) are…
The mean and -1 standard deviation	34.13% of all the cases under the curve	From 90 to 100
-1 and -2 standard deviations	13.59% of all the cases under the curve	From 80 to 90
-2 and -3 standard deviations	2.15% of all the cases under the curve	From 70 to 80
-3 standard deviations and below	0.13% of all the cases under the curve	Below 70

What’s Under the Curve?

A standard score that is the result of dividing the amount that a raw score differs from the mean of the distribution by the standard deviation.

What about those symbols?

The z Score

What about those symbols?

the z score

the individual score

the mean of the distribution

the distribution standard deviation

The z Score

Scores below the mean are negative (left of the mean), and those above are positive (right of the mean)

A z score is the number of standard deviations from the mean

z scores across different distributions are comparable

The z Score

Using Excel to Compute z Score

The areas of the curve that are covered by different z scores also represent the probability of a certain score occurring.

So try this one…

In a distribution with a mean of 100 and a standard deviation of 10, what is the probability that one score will be 110 or above?

What z Scores Represent

In a distribution with a mean of 100 and a standard deviation of 10, what is the probability that one score will be 110 or above?

84% of all scores fall below a z score of +1 (50% below the mean and 34% above the mean).

16% of all scores fall above a z score of +1 (100% -84% = 16%)

What z Scores Represent

How to Figure Out the Probability

STANDARDIZE a Raw Score

In a distribution with a mean of 100 and a standard deviation of 10, what is the area between a score of 110 and 125?

Compute the individual z scores for the two raw scores

Finding the Area Between Two Scores

Find (using Table B.1) the area between the mean and the z score of +1 = 34.13%

Find (using Table B.1) the area between the mean and the z score of +2.5 = 49.38%

For the area between the two scores, subtract the smaller from the larger

49.38% – 34.13% = 15.25%

Finding the Area Between Two Scores

Using a Drawing to Determine the Area Between Two Scores

Computes the probability with a function

Table B.1 is not required

NORM.S.DIST(z, cumulative)

z is the z score for which you want the probability

cumulative is a logical value

Almost always True

Using Excel for Probability

Knowing the probability that a z score will occur can help you determine how extreme a z score you can expect before determining that a factor other than chance produced the outcome

Keep in mind…

z scores are typically reserved for populations.

What z Scores Really Represent

()

11010010

1010

====+

12510025

2.5

1010

====+