Statistics Recording the results from our studies. Must use a common language so we all know what we...

Statistics

• Recording the results from our studies.

• Must use a common language so we all know what we are talking about.

Inferential Statistics

• Determine whether findings from a study can be applied to a larger population

• This is why you want your sample to represent the population as much as possible.

How do we do this?

Inferential Statistics

Inferential statistical tests: •Chi square•T-test•ANOVA

All of these tests give us a p value. It tells us how statistically significant our results are.

A p value = .05 or less means that results are statistically significant.

Descriptive Statistics

• Just describes sets of data.

• You might create a frequency distribution.

• Frequency polygons or histograms.

Measures of Central Tendency (know this term)

Mean = average of all scores or observations

Median = the middle number when all scores are sorted from highest to lowest

Mode = the score that appears most frequently in the data.

Measures of Central TendencyWatch out for extreme scores or outliers.

$25,000-Pam $25,000- Kevin$25,000- Angela$100,000- Andy$100,000- Dwight$200,000- Jim$300,000- Michael

Let’s look at the salaries of the employees at Dunder Mifflen Paper in Scranton:

• The median salary looks good at $100,000.

• The mean salary also looks good at about $110,000.

• But the mode salary is only $25,000.

• Maybe not the best place to work.

• Then again living in Scranton is kind of cheap.

Normal Distribution

• In a normal distribution, the mean, median and mode are all the same.

Distributions

• Outliers skew distributions.

• If group has one high score, the curve has a positive skew (contains more low scores)

• If a group has a low outlier, the curve has a negative skew (contains more high scores)

Median

Median

Mean

Mean

Important Idea

• The larger your sample size, the more likely it is your data will resemble a normal curve (because outliers will be mitigated).

Seeing Statistics – Click on Contents – Go to 7.1(http://www.seeingstatistics.com/)

Other measures of variability

• Range: distance from highest to lowest scores.

• Standard Deviation: the variance of scores around the mean.

• The higher the variance or SD, the more spread out the distribution is.

• Do scientists want a big or small SD?

Dwayne Wade and Kobe may both score 26 ppg (same mean).But their SDs are very different.

68% are within one standard deviation95% are within 2 standard deviations99.7 are within 3 standard deviations

CorrelationRemember the scatter plots!

Positive Correlation (bottom left to upper right)

Negative Correlation (upper left to bottom right)

Practice Question #1

1.Which of the following events is the most probable?

 A)flipping 6 or more heads in 10 coin flipsB)flipping 60 or more heads in 100 coin flipsC)flipping 600 or more heads in 1000 coin flipsD) All these results are equally probable.

Practice Question #2

1. For which of the following distributions of scores would the median most clearly be a more appropriate measure of central tendency than the mean?

 A)10, 22, 8, 9, 6B)12, 6, 8, 5, 4C)12, 15, 12, 9, 12D)23, 7, 3, 27, 16

What would be another way of asking this question?

Practice Question #3

3. Professor Connolly uses a scatterplot to display the relationship between students' intelligence test scores and the number of failing grades they have received. The points on the plot are most likely clustered in a pattern that:

 A)resembles a Ushaped curve.B)extends from the upper left to the lower right of the

plot.C)resembles a bellshaped curve.D) extends from the lower left to the upper right

of the plot.

Practice Question #4

4. In a single day, 45 babies were born in hospital X, 65 babies in hospital Y, and 25 babies in hospital Z. At which hospital is there the greatest probability that more than 60 percent of the babies are of the same sex?

 A)hospital X B)hospital YC)hospital ZD) The probability is the same at all three

hospitals.

Practice Question #5

5. Approximately what percentage of the cases represented by the normal curve fall between –3 and +3 standard deviations from the mean?

 A)34B)68C)95D) 100

Practice Question #6

6. When Mr. Adams calculated his students' algebra test scores, he noticed that two students had extremely low scores. Which measure of central tendency is affected most by the scores of these two students?

 A)meanB)standard deviationC)modeD) median

Practice Question #7

7. If IQ scores are normally distributed, having a mean of 100 and a standard deviation of 15, approximately what percentage of people have IQ scores somewhere between 70 and 130?

 A)34B)50C)68D) 95

Practice Question #8

8. What is the standard deviation if the variance is equal to 36?

 A)4B)5C)6D)9E)36