Introduction

1. Need for statistics

- answering research questions

- Draw inferences = inferential statistics

i. population -> parameters

ii. Sample -> statistics

2. Variables

- Dependent

- Independent

3. Notation

X, Y

N

Xi

X_{1}

4. Measurement Scales

- nominal

- ordinal

- Interval

- Ratio

5. Limits of Measurement

- Discrete variable

- Continuous variable

- Real Limits

Frequency Distributions

1. Frequency Distributions--Question answered: How many people got this score

- Used to organize/summarize data to allow easy examination of it

- Example of 100 point exam:

100.00 1

99.00 2

95.00 2

90.00 2

87.00 1

83.00 1

77.00 1

75.00 1

74.00 1

70.00 3

67.00 2

66.00 5

64.00 2

55.00 2

50.00 3

43.00 1

3. Percentiles--Question answered: What score does a certain percentage of people fall below? (Or what's the cutoff point?)

- Percentile: the score below which a specified percentage of scores fall

Percentile | Value |

25 | 64.286 |

50 | 68.2 |

90 | 97 |

3. Graphing Frequency Distributions

A. Basic Rules

1. Scores go on X, Frequencies on Y

2. Both axes start of at O; if not break the axis

3. Y about 3/4 of X (see p. 50)

4. Label each axis

B. Bar graph of nominal, ordinal data

1. Bars don't touch

2. Height is frequency

CATEGORY OF WORKER | WEEKLY EARNINGS ($) |

Professional, tech. | 277 |

Managers | 302 |

Sales workers | 225 |

Clerical workers | 167 |

Craftspeople | 259 |

C. Histogram

1. Interval/ratio data

2. Bars for each interval from lower to upper limit

3. Bars touch (continuous variables)

4. Midpoint is marked on X axis

D. Frequency Polygon

1. Interval/ratio data

2. Like histogram except midpoints are plotted and joined with straight lines

3. Close off with interval above and below to zero (gives impression of the "shape" of the distribution)

E. Shapes of Frequency distributions--tell us about data

1. Symmetrical: if when folded in half the two sides coincide

e.g., bell shaped/normal curve

2. Skewed: if not symmetrical

a. positive=tail at the positive end

b. negative=tail at the negative end