2.4 - A Statistical Primer

Question 1

Descriptive Statistics

Answer 1

a set of techniques used to organization, summarize, and interpret data

Question 2

Statistics used to describe and understand the data:

Answer 2

Frequency, central tendency, variability

Question 3

Data Distribution

Answer 3

1) whether some scores occurred more often than others

2) whether all the scores were clumped in the middle or more evenly spaced across the whole range

Question 4

Histogram

Answer 4

Bar graph

*vertical axis shows the frequency

Question 5

Frequency

Answer 5

the number of observations that fall within a certain category or range of scores

Question 6

Normal Distribution (Bell Curve)

Answer 6

a symmetrical distribution with values clustered around a central, mean value

Question 7

Negatively Skewed Distribution

Answer 7

a distribution in which the curve has an extended tail to the left of the cluster

Question 8

Positively Skewed Distribution

Answer 8

a distribution in which the curve has an extended tail to the right of the cluster

Question 9

Skews occur because?

Answer 9

there is an upper or lower limit to the data

(ex. person cannot take less than 0 mins on a quiz, curve of quiz time cannot continue indefinitely to the left, beyond the 0 point)

Question 10

Central Tendency

Answer 10

a measure of the central point of distribution

*measured usually by the mean, but there are exceptions

Question 11

Three different measures of Central Tendency

Answer 11

mean, median, mode

Question 12

Mean

Answer 12

the arithmetic average of set numbers

ex. class averages

Question 13

Median

Answer 13

the 50th percentile - the point on the horizontal axis at which 50% of all observations are lower, and 50% of all observations are higher

Question 14

Mode

Answer 14

the category with the highest frequency (category w/ most observations)

*measure that is used least

Question 15

Which to use to calculate central tendency when mean, median, and mode are equal?

Answer 15

Normally distributed data - Mean

Mode = measure that is used least, provides less info than other two, used when dealing w/ categories of data (ex. when you vote for a candidate, the mode = candidate w/ most votes)

Skewed Data (Positively/Negatively) - median (extreme values have a large effect on mean but will not affect the median

*the longer the tail, the more the mean is pulled away from the centre of the curve

Question 16

Variability

Answer 16

the degree to which scores are dispersed in a distribution
(some are spread out, some are clustered)

Higher Variability = larger # of cases that are closer to the extreme ends of the continuum for that set data
(ex. lots of excellent AND poor students in one class)

Lower Variability = most scores are similar
(ex. call filled with all “B” students)

*can be caused by measurement errors, imperfect measurement tools, differences between participants in the study, characteristics of participants on that given day (ex. mood, fatigue levels)

Question 17

Standard Deviation

Answer 17

a measure of variability around the mean (estimate of the average distance from the mean)

*links central tendency and variability

Question 18

The ______ always marks the 50th percentile of the distribution.

Answer 18

median

Question 19

The ______ is a measure of variability around the mean of a distribution.

Answer 19

standard deviation

Question 20

A histogram is created that presents data on the number of mistakes made on a memory test by participants in a research study. The vertical axis indicates?

Answer 20

the frequency of errors made

Question 21

In a survey of recent graduates, your university reports that the mean salaries of the former students are positively skewed. What are the consequences of choosing the mean rather than the median or the mode in this case?

Answer 21

The mean is likely to provide a number that is higher than the largest cluster of scores

Question 22

Hypothesis Test

Answer 22

a statistical method of evaluating whether differences among groups are meaningful, or could have been arrived at by chance alone

Question 23

Statistical Significance

Answer 23

the means of the groups are father apart than you would expect them to be by random chance alone

• proposed by Ronald Fisher
• not used for limited numbers of potential participants

Question 24

Null Hypothesis & Experimental Hypothesis

Answer 24

Null = any differences between groups (or conditions) are due to chance

Experimental = assumes that any differences are due to a variable controlled by the experimenter

Question 25

P-value

Answer 25

the probability of the results being due to chance

lower p-value = decreased likelihood that results were a fluke, and therefor, an increased likelihood that it was a good experiment

Question 26

Ronald FIsher

Answer 26

• presented idea of significance testing, rejected null hypothesis
• p-value cut-off point = p

Question 27

Paul Meehl

Answer 27

• rejects significance testing

- more testing = more chance of fluke, p-value standard must be decreased as # of tests increase

Question 28

Jacob Cohen

Answer 28

• developed power analysis
• goal to calculate effect sizes = whether difference is statistically small or large
• effect sizes allow researchers to adjust how much they believe that their hypothesis is true

Question 29

A hypothesis test is conducted after an experiment to?

A) determine whether the two groups in the study are exactly the same
B) determine how well the two groups are correlated
C) see if the groups are significantly different, as opposed to being different due to chance
D) summarize the distribution using a single score

Answer 29

see if the groups are significantly different, as opposed to being different due to chance

Question 30

Imagine an experiment where the mean of the experimental group is 50 and the mean of the control group is 40. Given that the two means are obviously different, is it still possible for a researcher to say that the two groups are not significantly different?

A) Yes, the two groups could overlap so much that the difference was not significant
B)Yes, if the difference was not predicted by the hypothesis
C) No, because the two groups are so far apart that the difference must be significant
D) No, in statistics a difference of 10 points is just enough to be significant

Answer 30

Yes, the two groups could overlap so much that the difference was not significant